Okay. Okay. Okay. Okay. Well, good evening. Welcome to the Amherst Board of Health meeting on March 9, 2023 and pursuant to Chapter 20 of the acts of 2021. This meeting of the Board of Health will be conducted via remote means members of the public who wish to access the meeting may do so by following the instructions on the Board of Health's posted agenda via Zoom or by a post to telephone number available on our website. No in-person attendance of members of the public will be permitted, but every effort will be made to ensure that the public can adequately access proceedings in real time via technological means. We will post on the Board of Health website a recording of the proceedings as soon as technologically possible after the meeting. All approved minutes of the Board of Health meetings are also posted on our website. I will now open the meeting with the roll call. So Maureen. Laura Mills. Laura. She's muted. Can you unmute Lauren? Yes, I'm here. Okay, great. Primal and there. Here. And Nancy Gilbert here. So far we don't have Tim. Also in attendance is Ed Smith. And Jennifer Brown of the health department and inspections. So the first thing on our agenda is review the minutes of January 12th because Lauren lost contact last. Meeting and we could not approve the minutes. And then we'll do the February minutes. So first are the January 12th minutes. Does anyone have any comments? I looked at this a while ago, but I don't recall any concerns. Yes. Okay. I don't have any premise. I may have a motion to accept the January 12th minutes. I'll move to accept the January 12th minutes. And a second. I'll second it. Although. Maureen. Yes. Hi. Lauren. Yes. Yes. Okay. And Tim is absent, but he also missed the. January meeting minutes. The next are our February 9th minutes. I looked at them and did not see anything. Does anyone. Have any comments. They have any changes. Any questions or additions on the February 9th minutes. No. Okay. May have a motion to accept the February 9th minutes. Motion to accept. I'll second. Then first. Seconded and now. For accepting them. Okay. Maureen. Hi. Lauren. Yes. And Nancy Gilbert. I, so they have been accepted. Next on the agenda are in public comment. I don't see any attendees. So I don't think we'll have any public comment. Okay. Okay. And the first. Item is all business. And I have the community assessment. And the students are working hard. They've been doing. Key informant slash stakeholder interviews. They're having trouble setting up. Listening sessions. I know they've worked with Lauren. They have a date. They've had one listening session at the senior center. They will be having another listening session with crests. And then they're trying to set up a few more listening sessions. They're also planning to organize their data for the report using healthy people. 2030 social determinants of health. And there's a wheel. They're planning to organize their data. They're planning to organize their data. They're planning to organize that. Economic stability. Education access and quality healthcare access and quality neighborhood and built environments. And social and community context. That's how the social determinants are organized now under healthy people. 2030. So I will keep you abreast. Thank you. Thank you. So the agenda is body arts. Establishment. I went over some. Regulations and morning has spent a lot of time going over. Or other. Board of health regulations for more updated ones. Do you have anything to say, Maureen? I think that was based on your list of, of things that came to your attention, but also things that I. I mean, it looked into as I was thinking about this. Clearly just plopping in a section on. A guest artist. Is may not be what we want to do. We could do that. I sent a couple of. They're very short. They're very short. They're very short. They're very short. They explain how a guest artist might be qualified to come and spend two weeks with another. In a, in a, in Amherst establishment. Twice a year. For a small license fee. But we really haven't looked at these since 2008. I'm on my iPad, so I don't have everything in front of me. But there was some. Some of the items that I think would be important, like requiring a photo ID for. Clients and. Practitioners and for documentation for the. The parents and the child, if it's a person under 18. You know, some of those, those are simple and probably pretty important to make sure where we have. The information about the person who's doing this and the person who's having it done. There are ways to open this up in a much bigger way in North Hampton and some other communities. They actually have a program of apprenticeship. That in those are defined and what, what's required of an apprentice and what's required of a trainer. And you know, it's, it's a lot of regulation. It's, it's a lot of regulation. It's a lot of regulation. It's a lot of regulation. We could copy, you know, we could base it off of some of those existing regulations, but is that something. We want to go toward. There are also other health regulations in different places, like in Provincetown, where I expect they have a lot of body artists. They're not, they're the same on the hepatitis screening as, as everyone else. But, but there are some other additional health screenings. In North Hampton, they're requiring a policy and procedure manual in addition to having a copy of the regulations on hand. There are some increased requirements of, on the use of the autoclave and it assuring that it's working properly. So it's, it's kind of a lot. And there's a, there's another section where Amherst says, here's what you can do. Like you can pierce an eyebrow or a nose or a ear, a navel or a nipple. And a lot of other places say what you can't do. And a lot of that is involves genital piercing and, but also like neck and back and chest. And my sense is it's easier to say what you can do than think of all the things you can't do. You know, just because people are pretty inventive and they might want to do things that we might want to have them do. I guess I wanted to bring this up and think about what people, how people feel about where we want to go with this. Any, I thought, any thoughts. I also have a concern about our regulations and how are we enforcing them? Can we enforce everything? Do we need to? Who, and do you go in inspect tattoo parlors? I have currently Susan Malone. Does she go every year to check? Between the two of us we have, I believe it's possible we miss one of the pandemic years. But yeah. Yeah, an annual inspection and to make sure that the establishment and the practitioners renew their licenses. Currently, we have one establishment with one practitioner and the owner of the shop. He had two or three other people. And I think during the pandemic business fell off quite a bit. I think somebody left the area. People moved to other shops East Hampton, especially seems to be on the rise for a location for shops. And North Hampton's always been quite strong for shops. As we add to the regulations, how does that affect you and Susan as inspectors? I think that the things that you're talking about would be more clear clarifications of. I don't think that there would be too much dispute. Trying to remember Steven, the owner of the current shop in Amherst is quite interested in if there's an opportunity for him to help or be involved. I'm sure he would be a trustee. He's experienced these work in several towns. And he's been. He has a consistently good record of maintaining the shop and keeping the people that are working in the shop online. There's one thing about the shops that I'll just throw out is that they operate a little bit like some of the delivery companies in that they call themselves. I think independent contractors. Working within the shop. And that's more for I think their purposes. I don't know if that's the case. Maybe tax wise. But. It's just an oddity. We've still make sure that they all have their proper licenses. The facility is. That's hasn't been. That's common practice. And the other. It seems surprising to me that this isn't something that is licensed by the state. The practitioners. I mean, aren't hairdressers and barbers licensed by the state? I mean, I think it's more. Invasive than any of those things. I'm not sure the history behind that tattoo powers have been around for a long time, but. But the state. I think it's reluctant to take on any more inspections. You can avoid it. Yeah. And the training and things it's not well, or is well organized. This may be like other states like Connecticut or whatever where they have a. Different way of looking at it. Massachusetts is newer to. Allowing tattoo parlors because I know my son around 2000. Got a tattoo and he had to go to Connecticut. So it's only about 2002 that Massachusetts allowed tattoo parlors. I would have to check the, the exact date. So it's a newer entity in Massachusetts and in Connecticut. I was just wondering. From what you said, Maureen. Is it. What is the reasons for the client having the picture ID and. Isn't it. Better to also say what you cannot do because if you don't state what you cannot pierce. Then can the. Pat to artists. Just. It anyway, or is it like, I guess. Just my thinking. As you said, the state regulations, I don't know what they. They regulate, but if it's not. If the town regulations don't state what cannot be pierced. Is that allowed them to pierce whatever they want to pierce or. No, but actually says you can only pierce these things. And nothing else, basically. So I think. I think people take. I think you could argue it either way, but. But it seems clear to me that you can't. From our regulations that you can't do any sort of genital pierce thing. And that's a lot of those things that are prescribed in. Other. Other towns, but. You know, so. I guess I look at it as we, it's, it seems like. You could come up with something that's not. Written down and that wouldn't be a good idea that you wouldn't think of writing and saying, no, you can't do that. But rather than say you can pierce these different body parts. And I do not believe that our existing tattoo parlor. They do not do piercings at this time. Right, right. But I guess we need, if we're going to do this. Yeah, we do. We do. Correctly, because another parlor might. Do piercings. Yeah. Or they might add up another independent contractor who wants to do the take on the piercings. Yeah, and they have announced. Yeah. So. So what is the sense of the need for the, the apprentice. Apprentice program. I know. I know the establishment isn't asking for that particularly. Is that another thing we want to have in preparation for a new or a different establishment or this. Person deciding to do a little bit more. I mean, it doesn't hurt anything, but it's a lot of. It's a lot of a lot of regulation to kind of just look at. And review and try to. Fine tune. We actually. I'm sorry. I was going to say we actually did work out an apprenticeship arrangement with Steven Lambert. His last name is. Who's the owner of a shop. He did have somebody working there. Maybe. For a year or two years ago. Who. Steven took all responsibility was there all the time that this person was there. We gave them sort of a provisional. License. And it worked out well, except for Steven. A fellow left to go to another shop when he finished. But it, but it was. I mean, we thought that Steven had the makings of a good teacher. That was a good. Yeah. We. Yeah. So maybe we should maybe put that in there. I mean, it might encourage more businesses to be in town. And that's one of the things we. Want to do. I mean. So. I don't have any problems. Just maybe. You know, putting my. My head around it and try to get a. A rough draft of all of that kind of regulation kind of pulling from different places. That we can all take a look at that. At some time, perhaps as soon as the next meeting. I don't know how anxious they are to get the visiting artists in there. I don't know. I don't know. I don't know. I don't know. I don't know the time that the turnaround from. From meeting to meeting. Any other thoughts. You know, use as much from North Hampton. Don't reinvent that wheel. No, I know. Well, there's, there's a kind of funky. Actually, there's some like typos and things that don't connect. Then. You know, I know what that happens. I don't know. I don't know. I don't know. I don't know. I don't know. I looked at Melrose. I can't remember. I looked at about. Eight different towns that had. East Hampton is based off of North Hampton, but it seems a little cleaner. Maybe a little less. Complex. You know, I don't know that a policy and procedure manual adds more to. The regulations themselves, which are quite detailed. I don't know. I don't know. I don't know. I don't know. All of that. So. And I do like the idea of having hepatitis. That the practitioner is having hepatitis. Immunization. I think. For safety. Well, nobody required. Nobody's required that it's all been, you have to have the educated. It's like the. The OSHA training and. I thought North Hampton had. I thought North Hampton had. Be in Worcester had. You needed to have your hepatitis immunizations. I don't think I saw it that it was required, but I'll double check. I mean, it might have been Worcester. And I don't have that pile of stuff here with me. Yeah. I think it's hard to be choir. That kind of. I don't know. But. I don't think North Hampton did. I think there was a, I don't think it was required. I don't think it was required. I don't think it said it strongly recommended. And then there was like, that was. Item A and then item B. If you do have the hepatitis B. So I felt like when I read it, it told me one thing. And then sort of. Jump to another. Williams town has, I think a requirement for. Happy. That's the only one I saw. Thought I saw. So it's hot. It's not. I mean, it makes sense. I don't know. I don't know. I don't know. We can, that's something I guess to look at a little more closely. Maybe to try to decide about that. You know, depending on how old the people are, it doesn't really. Work that well. The vaccine and older people, but anyway. That's neither here nor there. So I will take another stab at, at some of this and come, come back to that. And then we'll go back to that. That we could look at. And compare our regulations. I don't know if anybody. No, I don't think I sent out the whole thing. I put together. Something where I went through our regulation and added whatever was in North Hampton. That was more than what we had in. In. Side, like in a separate color. In the same paragraphs. I don't know. I don't know. I don't know. I don't know. I don't know. To try to. Combine the two. I could send that draft out, but it's kind of a messy thing. I, I. I tried looking at and one of them. The stuff came out black and I couldn't read everything. And so I just. Yeah, it's hard to copy. It's hard to get a editable copy, but. Like I was able to do that. I don't know. I don't know. I'll send some of it along to Prem. She has time to take a look at that perhaps. And we'll see where we are. Okay. Okay. Thank you. So now we're going to move on to new business. And first thing in new business is our. Housing code amendments and overview. So thank you. This is. Something that when I took the state housing training 12 years ago, it was just around the corner. And we've just turned the corner and it's arrived or will arrive. The estimates. Get early in April. So maybe April 1st, but sometime in April for sure. And there are. I think a lot of the changes are. More bringing the code language sort of. To date, but it also. Catches up with some things that have developed. In the last 50, 50 so years that the roads been around. So I'm going to share my screen and try to. I'm not, I'm not going to jump around too much. I'm going to end up on my notes and stay there. But. Let me see if I can first pull up. The original code. Which this is. This is the code that John Thompson and Susan Malone and I use. Weekly, if not daily. On housing inspections in town. And with. The reason actually that there are so many of us doing. Housing is because Amherst's. You know, nature is a college town with not enough on campus housing is that there's a lot. In town and there are a lot of. These relationships between tenant will am or come and go. I don't know what the average tendency in town is, but it's probably between one and two years. And if you go maybe to Northampton or some other. Town with their own peculiar to their economy circumstances. I imagine there. Most of them are there for a longer period of time. So there's a lot of. Charning and flux and our housing market. And so we often are mediating. Housing. Disputes or concerns, complaints and lack of. Maintenance, perhaps, or we do certainly apply the code to tenants when that's appropriate when the landlords are looking for help. Some of those not cleaning who's being destructive to their unit. But this is the, the sort of old fashioned sounding minimum standards of fitness for human habitation. The sanitary code the housing code it's often called 105 CMI 410. And this, I think came out in the early 70s. And it does a pretty good job. Of defining and laying out. Issues that, you know, can arise. And it's meant to be minimum standards. So everything above this is fine. It's, you know, it's extra that might not be aesthetics. I feel pretty necessary, but this is the baseline that we approve to. So let's see if I can go to the other, the new code. Which unfortunately, you know, the numbers changed quite a bit. So that will make it a lot harder for us to, to, to get with that. That's all right. It's a little more organized in a way. I think it will help us find issues when we're trying to cite somebody. We're trying to figure out why a leaking faucet is a problem. You know, we can go to the plumbing section, section, section, whether it's in the kitchen or. But I made some notes. That's what I should go to. One my apologies one second. I'm lost. Okay. Can you see. Let me know if there's anything I can do on my end. Okay. There we go. Yeah. Okay. So a few things they told us. John Susan. I've all attended trainings now from the. State. Board of. Community sanitation. Question. I'd always had this. How far does the code go back originally to 1960. And it was funded in 1972. It was followed after that by adoption statewide. A standardized building code. And because it's not listed as a subsidiary code, it's always been, I think felt as. Separate. And, you know, complimentary, but it stands on its own. And I'll, I just highlighted some notes that have occurred to me as I'm reading it. I'm sure as we put it into practice, we'll see more. Useful differences. There are some challenges. One thing that we've always had a friend. Is the could be original code was written very much with violations of the owner in mind. There was a limited number of responsibilities. Of the tenant. They're important. But. The predominant. Number. Is. With the owner. But affected persons is now a phrase that we could use. It is used in a language because it's a little hard to hear you. Oh, I'm sorry. Oh, that's, that's even better. Yeah. It's my hand. Anyway, some of the violations can occur equally, whether it's the tenant or the owner. So. Another place. Tests used to not. A separate citation for. Spiders. And we occasionally get this academic argument. That. Can't begin with the station. But. Other. Categorized. Test. Types from the. The old code didn't deal with recycling at all. And now most communities, all communities have. Quite a few regulations. About recyclables. Makes it easier for us to cite. Issues that are. You know. But something to do with not, not garbage, not. Useful possessions, but. This other category. Residents now. Includes all the structures on a property. Which in the past that wasn't really clear. You could have a rental house with a falling down garage. Or a falling down outbuilding, which might present a hazard. You had to make a more complicated argument that this represented. An issue on a property. But now. By including all structures. It's going to be easier to cite for maintenance of buildings. I don't think it necessarily means that every little structure has to be in perfect shape. But if it's not. It's not going to be maintained fit to use. It needs to be secured so that it doesn't present hazard. The old code didn't really deal with temporary shelters at all. And that's something that does come up now. And that will help with shelters that are maintained in Amherst, for example. And can you speak up a little bit please? Yes, I'm sorry. Thanks. Kitchen facilities. There was not a definition in the past for what constituted the appliances. It was mentioned that, you know, you have to have a range. But now a size of the range is there. And for the first time, it includes a freezer. Plus it's excluded. From a lease. In the past, a landlord just had to provide a space for the refrigerator. And it's not an outlet. Convenient to that space. These can still be excluded in the lease if it's spelled out. And the 10 degrees. So there's some flexibility. I'm sure that some of the complexes that don't offer something. We'll put that in which instead of just assuming that the code is not checking to see whether they're providing the refrigerator. And that's the direction how water. There actually were some discrepancies with the plumbing code. And those have been cleaned up. You don't want us hot water. In a bathtub or shower or scalding reasons. And that's the way plumbing fixtures are meant to keep. The temperature to 120 or below. But also above 110 so it's. The cleaning. For the first time. Eating systems. Don't. We now know what to say. Wood and pellet stoves and space heaters. Fireplaces. They aren't prohibited. They just can't be dependent on. There's not. You can't. Tenant can choose to use a wood stove, say to heat, but they have to be provided with a permanent. Install system. Not as backup, but it's a primary the backup. Woodstick. So that ended up second. The next one. Is important to the board of health. You've entertained. I'm sorry. Request for the answers in the past from the car. For the beginning of the heating system. And now the language. Has moved up the date in June 1st. Now you can. They was June 15. Sorry. Is now June 1st, but you can alter it to May 15. As easily as say in the May meeting. Looking at the upcoming weather. This is going to be a born May. And people are going to be wanting to switch from heat. To air conditioning sooner. And you can post that on the website. It's done. You don't have to entertain. No, a hearing. From anybody who's petitioning you for that. So that, I think. That takes something potentially. Down to owners installation maintenance and repair responsibilities. One issue that we've had in the past is a landlord. Leaving a mess after they make a repair. And finally they have to clean up after themselves. You know, the wording is there. The job. Is done when it's clean. And also when things have dried. In the next one, there's this is a complimentary occupants. Citation here. Some things the owner installs are necessary. Some things the occupant may bring in that are optional. And what are highlighted there, the air conditioners. And the microwave ovens are common. Things for us to have issues around their conditioners that are not secured in windows. Last week I did a bat inspection of that complaint. About how are the bats getting into a townhouse unit. And I found an issue with the owners applied air conditioner. The grill was loose on the outside, leaving a gap. But the tenants had also brought in their own air conditioner for another benefit. They had it installed. Put in the foam stripping that seals between the sashes. And that actually is important to save energy, but also to exclude tests. So, you know, the conclusion was we don't know which one it was, but they both have to be fixed. And that's kind of a, you know, real life, you know, issue that we're trying to use the birds to mediate. It's now explicit in the means of egress that all residents have to have to be gross. Used to be more like as many as are sufficient. And sufficient is two or more. Which helps closets need like pictures. And the light in the room is not bright enough. That's new. That may or may not have much effect. But the next one, the interesting thing there is what we write or do is to correct. We give our copy of our inspection sheet to the tenant to the landlord. We're supposed to include the tenants benefit the notice of occupants rights and that includes things like. If a landlord has not corrected. An issue that a health inspector has cited. If it goes beyond the repair time allowed, the tenant can withhold rent, for example, the tenant can also use their own money to make the repair and then withhold that from the rent, you know, the costs of the repair. So those rights are humiliated sheet. And now the landlords have to have sheet, which is. A positive thing. I mentioned earlier that homeless shelters are in the code now for the first time. They'll come up again in a minute with some pest requirements. The next one, number 500. This is one of the few ones where the numbers stayed the same between the new and old code. The owner's responsibility to maintain building and structural elements. This is probably the most commonly used section of the code for housing. And now includes a section where. And this has been taken for best practices. To keep mold from a rising housing situation. The owner shall ensure surfaces have been dried within 48 hours. So when you have a flood. Massive leak in the house, you are. Engage a company like service master or somebody with big air system.  Level of moisture in sheet rock, say that stage or floor. And it's not. Easily done. It can be done. And it needs to be done. If you don't want to have to rip out a lot of molding. Building materials. The next one. Elimination tests. And that's still there. But there's an exception. The owner hasn't been. You know, keeping up with the entry point, say. In the basement and house itself, you know, the holes that the past made in the past. If those haven't been fixed. It's not on the tenant. To try to treat. Around those. Those violations just throw the responsibility back on the landlord. First you fix, you know, the source of a problem. The past itself. And also new. And this is where I mentioned in temporary shelters. There's language explicit or temporary shelters. With this letter F. When you. Turn over an apartment. You now have to inspect the past. The past that hasn't been explicit. Homeless shelters do have an exception from that because. They will have a pest management policy and periodic inspections in place. That'll be part of what allows them to. But in an individual. Unit. When I as a landlord turn over a unit, I have to go through. They can inspection. I have to document. I need to keep. Essentially evidence that. I am. Looking for pests. If I find the entry points. I'm eliminating. Documenting. And that they're available to you. To the board. Upon request. And I can ask for those as your agent. So as I'm doing inspections. So that. Actually. Another one that will help us. Amherst quite a bit. Is trash put out for collection. And trash cans left perpetually by the food, which is. One of our common problems. The code was kind of unrealistic in that. Said you could only put it out in the day of collection in the past. And now. You can put it out the day before. If it's in a pest-proof container. So not just a bag on the sidewalk. But. A bag in the trash can with the loop closed on the sidewalk. Next. Can't block. The right away. The travel. Lane. It's the road. It's the sidewalk. So. We're almost done. Let's see. 570. An interesting point here is that standing water. And decided. More easily now in the past as a. Issue. On a parcel of land. So. If someone's butter sale, creating a draining. And not being sent off. To a permeable area of the yard. It's just, you know, ponding and. Potentially causing problems. We can judge that to be so. And they can work. 620. Is mentioned something that's helpful about. We often get asked, do we do mold testing? We don't. We. Can use signs of more. Appearance. Of mold. As evidence that there's excessive. Excessive moisture. Present. But. We don't have to. We don't have to pay for environmental testing. Environmental testing is still not. Recognized in the state as being. A guideline. You know, like. Certain level. A specific type of mold. Found. Is not. Sightable. But we can use mold as an evidence that. The moisture level in my house is too high. And. Look for the source. Whatever it is. Water in the basement that's causing problems in the first floor. Then. This. The last section here. These are the things that could. Most likely bring a hearing to the board of health. And I thought I would just go over there. They really haven't changed. They used to be in the section that was number seven 50. Now it's 630, but it's the same title conditions deemed to endanger. Material. Health or safety. We used to have. Under the code. Three. Levels of citation. Something either need to get fixed within 24 hours. Within five hours. Or within 30 days. 30 days, for example, would be something like if. Someone needed to make a plaster repair. Say. That's not. An immediate danger. But. It's a deficiency by the code. And so we could fix the plaster. Do a second code. Paint it. And, you know, that easily fits into the days. But other things. And these are enumerated here. Much more immediate. There was a subcategory of these. That. Like the kitchen sink. If your kitchen sink was too small. You had five days to fix it. Now. You should know better. It's the message. And the code. And that's the message. And that's the message. That's the message. And so. You should know better. It's the message. And the code. And that's judged to be the same level of the issue. For the landlord to repair as these. But I'll just read these very quickly. Supply of water sufficient quantity pressure and temperature. Failure to provide.  The standard electrical facilities not being provided. Just a quick example of that we expected about seven or eight years ago. And the wiring was. Happily unsafe. It was aluminum wire in the house, which is, it's the only time that it was seen. And we called in the electrical inspector. And the house. And it was, you know, repaired. You know, as almost an emergency basis. Safe supply of water is essential. These are things again, that can condemn a house. Or, you know, lead to government nation. The limber disinfects. The lack of a toilet sink, shower, bathtub. Or sewage disposal system. Then the following things, these are the old used to be five days and other 24 hours. The sink. Cook top of them. The refrigerator and freezer. That's new to the code, but that's important. It's there. Adequate exits. Egress is very important. Security requirements. These are the locks and your windows and doors that keep you safe. There's a catch all section here about any. Sources of causes of sickness. Including carburetor rodents. Lead based paint. In terms of it being accessible to. Somebody under the age of six. There's another broad section here in the 12 roof foundation and defects that can expose the occupant to substantial danger. Number 13 is all about using proper. Technicians to do specific work. So not using unlicensed. Andy people. Instead of, you know, certified installers. Asbestos is still there still a problem. Smoke detectors. One of the most important things we do. I think this is more explicit now. We have a lot of railings and guards for steroids, porches, balconies. This actually is important in Amherst with a lot of student parties and vulnerable places. You know, the roof's up deck insufficiently built. You know, walkway leading up to a second floor unit. Tests. And then in the end, you know, the last two really just allow us to make a case that. Is listed above can be substantially dangerous. And could be used to take a 24 hour correction. Citation. And I didn't go into 710. There's a lot of this is brand new to us. Permit requirements for alternative housing. This gives the board of health some leeway, if somebody says proposing that to me or alternative housing. They used a houseboat as an example when we were doing training, that there's more leeway for you to consider. No, whether it's necessary to hold. Alternative forms of housing for the same standards as traditional housing. I think that is something we'll learn more about as we begin to work. Those things in town, not houseboats per se, but tiny houses. So I was a lot of talking in my part and I'd be happy to share. The new code hasn't really been published. It's not on master job, for example, yeah. I don't know, Jen, did that go out. Some of those attachments that I sent. I sent out and, you know, I'm just thinking I forgot to post this to the, the webpage. I apologize. I did send the climate to logical data to the, the board of health members. I thought that was interesting. So they did receive some of your documents. So we're looking out about, you know, putting this into effect. And maybe three weeks. Do the managers and owners have this information or how are they going to know? I've, we haven't sent out a specific mailing it. I've been talking about it with individual landlords as we work with them. Probably for the last three or four months. And I've shared it with a few, but I think that I'm kind of reluctant to send it out until the state publishes it. It might be good for us to send out a heads up. You know, this is coming. And it's also starting to appear in new sources. And I knew Greenfield's board of health department. Did put out. Sort of made up. They were the subject of a small news story. And a couple of state like landlords. Organizations have had a couple of articles online too. So yeah, it's spreading. But. The literal final code hasn't been propagated yet. I think probably we could have worked people. We will release that as soon as possible. Thank you so much, Ed. I really appreciate it. It sounds like it's really going to promote some healthy living, living conditions. Yeah, I'm sorry. A straight out 10 by 10. Thank you. Does anyone have any questions for Ed? You know, I have a. Okay. Okay. One is kind of random. I want to know, you said this is. Mainly for tenants. And landlords. What is the percentage of. Homes that are. Houses that are rented out. And just. Also the second question is the recycling. I still don't. I still in my mind don't understand. The plan for the zero waste and all those other initiatives, how it all correlates together. So I don't know if you can. Expound on that because I know. That for me, where I live, I do not see. Any recycling initiatives taking place. So I'm just wondering how. These new regulations will incorporate. Like you said, how will the landlords know. About these initiatives and these new regulations and specifically the recycling, how does, how, how will that be. Put into. Into place for, for renters. Let's see. So. Your first question, the percentage of homes and embers that are rented out as an interesting one. And I. I would really be guessing, but I will try to. I'll see if I can get. Yeah. And we have that in our. Community assessment data. I don't have it with me here, Lauren. I believe we sent that out when it was presented. And you can look in it. And it has by census tract. And. East Amherst and South Amherst have less. Renter occupied. Then central Amherst and North Amherst, but I don't have that data with me to tell you, but it's in that report, Lauren. And if you want. I can get it to you next week. Does that answer your question, Lauren? Yeah. Okay. What about the recycling? So members landlords through the residential rental registration program are required to. To certify to pledge to sign off each year when they renew, but they follow all applicable state and local regulations. So they are required to follow. Like the board of health recycling regulations in town. We. At present don't have a recycling coordinator or someone who's specifically doing that job. We had a grant funded job. A couple of years ago and that person. Was able to dedicate their time to going around and problem solving. You know, with. Mostly with complexes or larger landlords, but also with some smaller. You know. One off rentals. And I'm not sure if there was. If they could help them with their recycling program. There are a lot of right recycling regulations that we. Don't. Actively enforce. They're in place. And I think most places. They'll try to comply with them. But, you know, we are not.  Have the percentage. You know, below the allowed percentage of recycling. It's not something that we. You know, frankly. Have been asked to do, but. It's important, but it's hard to figure out where we would find the time to do that on an effective basis. We have to be able to do that. And we have to be able to do that on an effective basis. We have to be able to do that on an effective basis. Violating. We do on an individual basis. Bring it up. When say a rental house starts using their recycling toad.  Or just all for garbage. That will cycle. They're not doing it. They're. They're responsible for their tenants doing. The right thing, if you will. But I'm, I. Have never gone out and. You know, to continue loading. And we've had some. Manpower problems in some of the companies this year where. Trucks wouldn't come trucks were breaking down. They didn't have to repair people. They didn't have the drivers. And recycling. Bins that big complexes had to be used for trash. Just to safely contains that we had problems at Hampshire college from bears. When they weren't doing. So they'll seem to. Smooth out the companies are doing much, much better. So it's a challenging topic. I guess is what I'm trying to say. Yes. A little bit. I'm more thinking of like when you. Separate your life, for instance, if you have plastic bottles, if you separate your plastic bottles. But then. When you take it out, you might mix up.  In the recycling, like it seems like there's no. Here, like. Incentive to like. Keep the recyclable separate. And so I'm more asking about that, like. Is there. Is there a way to do that? And maybe I'm kind of off of the regulations and. More of the like incentive program, but. I'm just, I just, you know, I just see that. There's not. There could be more recycling if there was a clear way of recycling. And so that's mainly why I was asked. Yeah. I think DPW maybe could tell us more about. How successful recycling is, is working in town from their experience of the transportation. I know that the. It's very hard to sell recycling. If the company buying it. Is. Not judging it to be of a good quality. You know, if it's contaminated with garbage. With materials that shouldn't be on the recycling, then they just won't take it and it has to be. You know, disposed of. At cost. And I know that the prices have gone down on some of the recycling. So the incentives, the financial incentives there. Which would help a lot. Any other questions for. Thank you. Oh, you're welcome. Thanks for inviting me. Okay. That's all. That's a lot to digest. Yeah. Yeah. All right. Thanks. I'm going to take. Thank you. All right. Okay. Okay. Long time coming. And now it's going to be here. The geothermal well. Driller for rolling Ridge. And. Jen, you got an update that the well driller license certificate was updated. It was updated to people in their packets. To see, yeah. That was a good pickup. Okay. And I last week I went to the UMass public health and health science. Career fair. I had. Thought of going and asked Jen last year to go. I went. I told Jen, I don't think it's the best use of. Time. For our department or for the board now that I've been there. But I did make a contact with Megan. Megan Patton. Who is. I believe the, the, the Dean or the director of undergrad programs right now. And I'm going to meet with her. In two weeks, right after spring break. I'm going to talk about the school of public health. And the board of health. And she's new, fairly new to UMass. I think she's been there this year, second year. And so I'm just going to meet with her to talk about the board of health and the health department. And I'll let you know. What. What, what goes from there. But that was. That was interesting, but it was not a good use of time for our department. So Jim. That's that. That's it under new business. Directors update. Nancy, thank you for going to that. And did you like our new employees material? Yes. I had to return to you, but then I was leaving in the day. I was going to bring it. Yes. And yes, it was. It was interesting. It was great seeing students. Yeah. But I was giving them answering more questions for them about different things in the area. Then. So I felt like I was a faculty member there. Yeah. So I have some, I have six, six things I'm going to review in the director's. Update. This is the first time that I. Well, in three years, I haven't put. COVID update. Specifically. So I just thought I'd mention that of course we're going to continue to monitor it. But I just wanted to sort of blend it into. What I talked about in this section. As we are. Still in the pandemic section, sort of moving out into the endemic. Area of this pandemic. We're not there yet, but. We definitely are getting there, but we still have people in town vulnerable populations that are getting sick. We've had clusters of people that are being. That have been ill with COVID. And we've reached out to them. We still have a contact tracer or case management. Personnel Joseph of Boso on, on staff. And he's been working with town residents. So if anyone ever has any questions about home antigen test, rapid test, if you're positive, or if you've had an exposure, please feel free to, to speak to us about that. But this is also a reminder that three years ago today, we had our first case. Of COVID. And I don't remember the exact date, but it was around the 15th or so that we decided to shut things down and we were sent, we were sent home. So very dramatic. A lot obviously has gone on. In that time, we've had 10,652. Known cases of COVID since that time. So again, our surveillance data is down. We just don't have that PCR that we're counting. But we continue in the health department, as I'm sure you do, you know, residents and as board members to go some really good websites. I still go to the department of public health. Their interactive module is excellent. And they have a good wastewater module as well. And it's always good to see the, I think I forget what it's called the CDC now data. And you can see what, what. Oh my gosh. Blanking. What the, the type of. Of COVID is, is. It's trending right now. I'm so sorry. I'm just blanking on that. I'm going too fast. So we still have. Rapid antigen tests. We have lots to go around if anyone wants those. We are distributing here. At the health department, but we also are given to our partners like the Amherst. Survival center. There's still a great public health tool. So we really want people leveraging those. We still are continuing with our bay valent booster clinics. If it's someone that wants a second. Vaccine. In their series or the first vaccine, we can get that. Just let us know. We are having sort of a good turnout. People that maybe have been on the fence or coming in. But just to let you know that if you have your bivalent. Booster, then you're up to date. There's no other. New schedule or regimen on the immediate horizon that I'm aware of. So that's it for COVID. Does anyone have any questions about that? No, thank you. Okay. So. Then just moving into our. Public health nurse Olivia is doing some really exciting. Work and we're so happy to have her here in the health department. She's starting. Public health nursing nursing hours. She'll be starting that here in the bank center. She's going to be working or started already working with Haley in the senior center and she'll be offering those services. There. And then also she's been talking to Craig's doors. And they've been great partners to work with. She'll be going to the ILC and the university motor lodge. Twice a month and providing nursing services there. So we have the policy procedure where we're creating. And some of the things that she'll be offering. And we'll just start out slow and we'll see you there. But I think just getting in there and starting the relationship with people is really such a valuable tool. To really see some better health outcomes. The other thing is we have a new interpreter service in town. We've had them before, but this is through ARPA money. And we're happy to get this going. So it's through it. I out of Hartford and what we do is we've assigned, we have assigned pin numbers here in the health department. I've also shared it with Cress and the, um, and the senior center and it's on demand telephone service. And we've used it a few times for some dialects. We haven't understood for Spanish. And within seconds, we can do that. And so we've been able to do that. We've been able to do that a few times for some dialects. We haven't understood for Spanish. And within seconds, we can get people, um, uh, communicating with someone who speaks their language. Um, and it's just a great thing that we have. So we're happy to have that. Olivia was using it earlier with someone who speaks Portuguese. So it was really a great thing. We're very happy to have that. Um, um, the remote provision, uh, meeting is something that we need to, um, discuss. So I'm looking at my notes up here. So it originally it was supposed to end, um, March 31st, 2023. And we have not heard from the state yet. What's going to happen to that. We might hear on the 30th, but we should all be sort of prepared to, to see what happens with that. Um, um, the rules of the open meeting law, um, and be in person. Um, if there is new legislation or extension, um, um, the rules of the open meeting law, um, and be in person. Um, if there is new legislation or extension that we can continue on virtually. Um, so we should be preparing for April, um, to meet in person. But, um, I'll keep you updated as we get any more information. Did that make sense? Yes. Anyone have any questions on that? Yeah. And the word I was stumbling on before was variant. I used to use it seven times a day, 10 times a day. I'm blocking it up. Um, and then I want to talk about, um, so we have, um, we'll be losing some board members this year. Does anyone have any announcements? Um, who's going to be leaving? I'm, my term is up and because of term limits, I can't extend my time. Okay. Any other announcements? I believe I'm, I'm, um, my term is expiring in June. Is that right? So thank you, Lauren. I know I sent you an email. And both of you. For your time and hard work here, but we'll talk more about that and what you've added all, all of you. Both of you.  You know, I think when I think of things, it might be different from you, but I think about, um, the, you know, drinking water. I don't know, Lauren, that's something that's dear to your heart, but the civil and maybe environmental engineering, but that's something for you. Um, maybe if you can contribute to that conversation. Yeah, it's, uh, it's always very important to have a civil, um, or environmental and or, uh, engineer on the, the board for a while. We had to, um, it's what we need a doctor. And it's, uh, and it's very helpful, um, that we have a nurse. So right now you have two nurses with one coming off. So, so those areas are. And, um, with some public health background because. There's a learning curve and it's, um, much different than, I remember when I first went on the board of health in Williamsburg, um, I had been a nursing boy. It was a shock to me of how much I had to really learn and be aware of, um, for the board of health. Oh yeah. I remember that as well. Um, the last thing I want to talk about. Excuse me, um, is the, uh, Three St. Patrick Day weekend drinking event. You know, we used to not want to say Blarney blew out, but, uh, it was kind of receding and we hoped it was fainting, but I really felt like it came back in full force this year. And so it's something that I know we all take very seriously is preventing disease and harm. I mean, it makes us very proud to be doing that. And, uh, I feel like, you know, I personally as the health director have responsibility for creating, promoting a safe, healthy environment. And I think about the Blarney blowout. And my, the numbers that I have, um, we're 46 young adults were sent to the hospital with some kind of alcohol related. Um, illness. They're probably untold stories. Um, and it's such a serious thing. Now I think we can also flip it and say that there were some really good things. Like I'm hearing really good stories. About the, um, the, the, the celebration improved tenor from last year. Um, more responsibility. Um, and caring for each other. So it's sort of this mix of things, but I just think, um, you know, what happened this year to make it worse. Now.  Um, that's something that's been, um, Uh, around for a while. I don't think it can be linked expressly with the Blarney blowout, but it, it really contributed to the, the mayhem there. So this high alcohol drink and a rapid amount of time, this binge drinking is so destructive and harmful, um, to anybody. But when I think about our residents, you know, students are residents. Um, And just, um, about their, uh, it's legal. There's shared decision making, but I think it's, um, It's so harmful to anybody and these brains are developing brains. So I just want to ask if there's something that we, I feel as the director, I'm going to do something. Um, but I want to know if the board of health. Um, wants to make a statement or if there's any action you want to take. Right now. I mean, I know there's a lot to do. We briefly spoke about it, but I've been following this. And I've been very concerned. Um, and I think the board needs to make a statement or have it go in our minutes. Because, uh, the seriousness of Saturday. Compromise the health and safety of the students, not only of the students, but of our other residents, 46. Ambulance trips to the hospital. I think 28 ambulance trips. 20. Number of ambulance trips tied up our ambulances. And with the, um, Mutual aid, other ambulances in our surrounding town. So if a resident of Amherst, Hadley, North Hampton, I don't remember. I was looking who else helped respond. Um, That means those towns did not have. Full ambulance service if there was a true emergency for their residents. So that was a real concern of mine. I don't know what, what we can do. I don't know what other board members think, but, um, It, it, it's very serious for both the students and the residents. And it compromises all our health and safety. Other board members. Clearly it's a serious issue. You know, for, for what happened, but also going forward for the end of the semester, which goes well into the end of May. And I, I don't know if this pertains some difficult. Weekends, you know, the weather was terrible for this past weekend. For any kind of outdoor partying, which usually is a part of the problem. But, um, you know, it does make me anxious to think about what's going forward. I can see what you mass. Read about what you mass is trying to do and, you know, communicate with the students. I mean, really this is a student thing. Um, I don't know what we can do or say that's going to impact this really. This real trend that happened. I think people weren't familiar with didn't know how to regulate perhaps and really got a lot of people into more trouble than usual. But, um, it's a sort of annual event, but this one was again was worse. In terms of. The actual alcohol intake, I guess. In the town and university. Gave national attention. I have friends from the West Coast. What's happening at UMass. Yeah. No, it's a front page. A lot of paper. Um, I think my, um, I think the town council mentioned that. There were a lot of people from that came from outside of town. That made the crowds larger. A thousand people, you know, gathered in one area. Um, but no one, you know, died and however chaotic it was, I think it, it tests systems and sees how systems are doing well and how systems can be coordinated. So maybe in that sense, it was helpful and sometimes, you know, young people, they, they, they do certain irrational things. Um, because they know that there, there's some security, whether it was their friends that were looking out for them or they knew that, you know, there was emergency services that were available. Um, and like it is a planned event. So I just. Those were just my thoughts, but I don't know. Thank you. I mean, this didn't include any university authorized events. This was just, you know, a spontaneous sort of historical. Event, you know, the people want to bring back or relive or whatever. I did also read that there were more people perhaps from out of town, even though they weren't allowed to stay in the, in the dorms. I don't think the. You mess allowed.   Experience. So, you know, the fact that no one died were lucky and we don't know, you know, how that affected of like Nancy was saying other. Other services. Yeah. We did, they did call for a mutual aid, but also activated NEMA on this one. The Massachusetts amuse. Yes. And I think from pick and think, think this is from as far away as long meadow might've been involved. So it was a big deal. Now, historically there's a problem. So for a while. So maybe 20 years ago, I think it was like, you know, when the bars opened like at eight AM and people would go to bars and start drinking and throwing up all over downtown. So the bars reacted and they closed and they did not support Barney blow up. And then about nine or 10 years ago is when we had thousands of people that you couldn't. You couldn't drive down. Fearing street and many others because there were thousands of people that didn't. You know, you know, they responded and had programs on campus and they sort of kept it. In a little more in control. So here we go. Another 10 years. And so it seems like every eight to 10 years. It gets out of control and. There are elements to try and bring it back into control. Because it all needs to be addressed. And so I think the, the, the, the need to address the needs to address the health and safety. Not only of the students, but our residents and residents in the surrounding towns. And it needs to be addressed because it puts. Every day it puts the crest workers. It puts the police. It puts the fire department. The EMTs. It puts pressure on everybody. outcomes, but another time we can. So I don't think we can do anything, but I think we can make a statement that is concerned and hope that the town powers to be can work with the university to get this in control again. If anyone has ideas of what we as a board can do, or Jen for you, how we could support you as in the department. Oh, thank you. You know, I appreciate that. You know, I just want to start sort of assessing see what's going on and gather and analyze. I just hate to think that this just sort of goes by the wayside or we wait or we don't take action or we're too timid and something really detrimental happens again. And we didn't do anything. You know, I had this sort of thought it's like, man, can we can we outlaw those containers? You know, is there anything that the board can do? It's like, I don't like nips, but we can't, you know, what can we do? And I just don't know anything like that. I guess they said those are closed containers because they had a top on them. So I was okay. Right, you could potentially mix it yourself and say, hey, you know, as your alcohol content could be as low as you want it to be, right, when no one can slip anything into a closed container. But yeah, very clever. Yep. Yeah. And next year, who knows, it might be something else and my problem solved the board, but it'll be something else next year. I never heard of Borg until this weekend. They've been around apparently. Have you heard anything like that from your college health experience, recent college health experiences? Oh, not really. I was really concerned about this mixing vodka with electrolytes and that seemed to, you know, add a new twist to it. Sweet. But you know, I mean, I know drinking vodka is a problem at Smith, but not as much as it is apparently. I was just going to add, it was also mentioned that there was no counter activities on that day. And they're, you know, a way to help provide that. And also some of the parties, is there a difference between when the parties are on campus and when they're off campus? Because if they're off campus, I think there's more tendency for things to get out of control. But I don't know if the Board of Health can provide any ideas for counter activities or activities during the day. I believe most of this was all off campus. Although the counter activities still may benefit if there's some draw. I think in the past, they did do some serious attractive counter activities, which seemed to help some big act names come. And that's been pretty successful, I think in the past. There's also been, I think, like certain areas, well, Faring Street, I'm sure is one, but townhouse apartments seem to be an area that where this is a more of a problem. Maybe I don't know. And I'm not sure that there's anything you know that townhouse. And I heard that there were over a thousand people in the streets on North Whitney Street. I don't know if that's accurate. Yeah, that seemed like an unusual spot. South Whitney, I think that it's just that short street between the main street and lower part of Main Street. And a lot of North and South Whitney has turned into student rentals. I don't know. I mean, and I guess the police handled that well in a way that they didn't, you know, they watched it until it was a problem and then they took action. But if you can, I don't know if it's okay to party in the street, you know, that doesn't seem quite right. So I don't, I understand they're trying to work with what they have. And when there are that many people around, it's kind of tricky to handle it. Nine years ago was fearing. And I didn't go up and check what happened. But usually fearing northern part of Lincoln Avenue, nutting all down there. Barney Blowout weekend has two dozen cops from all over Western Massachusetts because they have their patrol cars from other towns and they're all standing on those corners starting like eight o'clock in the morning. So they've kept it off of fearing in those neighborhoods. So they just sort of, it's like whack-a-mole, they move. But you're right, the complex is in North Amherst tour. I've driven on pine. Is it my Meadow Street, I guess? Yeah. See a lot of action. Okay. So if it goes in our minutes that we're very concerned about the health and safety, and we do hope that the university in our town leaders can work out something for the safety. Also, paying for all of this, who pays for all these extra police and EMTs and ambulances in town? I don't think we do. So that's a huge cost. Yeah. Anything more on your report? No, thank you. I'm all set. Okay. There's absolutely no attendees, so I don't see any public comment. Topics not anticipated by the chair. Two of them we've sort of touched on. One is I got an email from Philip Avila, who is the co-chair of the Human Rights Commission, and he was reaching out to see if the Board of Health would be interested in joining a joint listening session with the Human Rights Commission, Affordable Housing Trust and Community Safety Social Justice Committee on the topic of affordable housing in Amherst and addressing complaints regarding landlords' upkeep of rentals. So I am going to a planning meeting with them on March 22nd. Would other people be interested in attending the listening session when it, and I will keep you up to date about the time and place of the listening session if anyone is interested in joining me at that listening session. I also spoke with Ed and I'm going to ask them to include Ed and the invitation for the listening session seeing that it's related to housing conditions. Possibly. I wanted to know the date, you know, whether it works or not. As soon as I get any more information, I'll post it to everybody. As I said, it's just in the planning stages right now and I just got this email. So I will keep you up to date. I wanted to let you know about that. And then I want to urge members, if they know of anyone who would be interested in serving on the board, to have them fill out the community activity form for the town so that we have a good number of people to interview for our two positions. And I hope that they can get filled in June so that come July 1st you have members because having only three members through the summer is going to be on the board with those interesting pieces. Only three of you starting July 1st. That's all I have. Does anyone have anything else they want to say for the good of the board or the health department? So thank you, everybody. Thank you, Jen. Thanks, Nancy Schroeder, who does a great job with our minutes and may have a motion. Oh, our next meeting is April 13th at 5.30 via Zoom unless we hear something else from the state. Yeah, I think if we post it, then right, so we'll wait and see. So it is April 13th. Can I say April 3rd, April 13th? And then we'll be kept up to date with what the state says about in person versus Zoom. I know hybrid isn't a possibility because of the cost and the technology needed. I think there's going to be some, but it'll be limited to you. Okay, may have a motion to adjourn. I move to adjourn. Second. I'll second that. Okay. Okay. I'm voting on favor. Maureen? Aye. Okay. Rembrandt? Aye. Lauren? Aye. So we will adjourn and thank you all once again for all your work. Thank you. You must appreciate it. Thank you. Thank you. Good night. Bye.


Then, historically, Riemann said, I do not like this idea. He did not say that, but essentially he said, why we should assume that the function should be bounded? So, his idea was very nice one. He said, intuitively seems, so this is a and this is b. He said, this is the graph of the function f of x and what you want to do? You want to capture the area below the graph of the function. So, this is the area that you want to capture. So, to capture this area, what you are doing is, you are trying to take upper sums and lower sums and trying to capture them in between. But let me do this way. Let me take any point in this. Take this height and take a small near by point c plus delta x. So, that will give me this. So, look at the area of this strip and try to imagine the whole area being made up of these thin strips. So, what is the area of this strip? You can take f of c into delta x and try to sum it up. And the idea of summation is same that you take partitions and make partitions finer and finer. But his idea is, instead of taking the minimum and the maximum in the sub-interval, take any value in that sub-interval and take any rectangle of that height. So, let me define that. So, definition, f is a function on a, b to r. So, let p be a partition x1 less than xn equal to b. Take any partition and choose any point c i belonging to x i minus 1 to x i. Take any point in the closed interval x i minus 1 to x i. Look at the height f of c i into the length. So, that is at the strip. Take the summation that gives you an approximate size of the area below the graph of the function. So, let us call it as spf. Now, there are two things one should observe. To define this sum, we do not have to assume f is bounded. We do not have to assume because we are looking at the value of the function at some point. So, we are taking the height of the function at that point into. So, right hand side is meaningful. So, this sum is well defined. We do not have to assume. At the same time, note that the point c i is a arbitrarily chosen point in the interval x i minus 1 to x i. You can take the left end point, you can take the right end point, you can take the midpoint or you can take any point. It does not matter. So, look at this and look at the limit norm of p going to 0. Make the partition finer and finer spf. So, if x is, we say f is, now we will call it as Riemann integrable if this limit. So, what is the meaning of this limit exists? Concept of a limit again, but norm of p going to 0, what is the meaning of this saying that limit exists? So, let me explain that because that is for every epsilon bigger, sorry, limit exists. So, first of all, what is the limit? One should say that there exists some number a belonging to R such that for every epsilon bigger than 0, there is a delta such that whenever the norm of the partition is less than delta, that implies this sum spf minus a is less than. For every choice, when p is a partition spf depends upon the choice. So, this says for every choice of those point c i, whatever choice you choose, you construct as spf, that should be close to the number a. That is what the limit means. So, you say it is integrable and this number a is called the integral. We should say Riemann integral for the time being because we have notion of integral coming from upper sums and lower sums called the Riemann integral. Now, once we give another way of interpreting the area, we should say that this way of defining the area is same as the one we have done by upper and lower sums. Both are same. There is no difference between them. So, let us prove that. But before even proving that important thing comes, namely that if f is Riemann integrable and if we want to prove that it is this integral is same as the one which we obtained from upper and lower, but that was defined only for bounded functions. So, there should be a theorem saying that if f is Riemann integrable implies f is a bounded function. So, let us prove that first.  In total, it seems quite okay because if the function is unbounded, those steps, areas, you can keep on increasing. That is one way of looking. But let us look at another way of proving this. So, f Riemann integrable implies there is a number a such that for every epsilon bigger than 0, there is a delta such that for every p, norm p less than delta implies spf minus a less than epsilon. The boundedness means what? We should be able to show that for every point x, mod of f of x is less than or equal to some constant. That is what we want to show. So, let us say this p is a partition. So, something say a is equal to x is 0, x1 less than x equal to b. Then for every point s i and t i, the spf requires choice of a point in between the interval x i minus 1 to x i. So, let me choose some point x i t i between x i minus 1 and x i. Then for every such choice, we have, so let me write corresponding spf f of s i x i minus 2 minus x i minus 1 sigma i equal to 1 to n minus a less than epsilon. That is the sum corresponding to the choice of s i. But let me also choose the sum corresponding to some other choice f of t i x i minus 2 x i minus 1 minus a less than epsilon. For two different choices, let us, so that is what it says. But we only want at a point, so let me make a choice. So, let us choose s i equal to t i. Let us try to take from these two equations. Let us subtract them and see what we get. Sigma of f of s i minus f of t i. If I subtract, I want to look at this. So, that means if I, what will I get less than, oh sorry, into that length of that interval. So, let me minus f of t i into x i minus x i minus 1. I want to estimate this quantity. So, I can add and subtract a. See, this is summation, this, the first term minus mod a, this minus mod a. So, summation f of s i minus capital A times this plus minus of that. So, I am saying this is less than 2 epsilon. Is that okay? Because what is the first term? Summation f of s i times this length. So, I can add minus capital A. So, I will get 1 epsilon by using triangle inequality. And that other one, I will combine it with the other one. So, triangle inequality. So, add and subtract capital A in this thing and use triangle inequality and use this 1 and 2. Is that okay? Or shall I write that step? So, let me probably, in case you feel uncomfortable, let me write.  Add and subtract. And now use triangle inequality. So, this will be less than or equal to absolute value of this plus absolute value of that and use 1 and 2 to get the required thing. So, this is less than 2 epsilon. So, let me call this as 3. So, in this 3, let us take s i equal to t i for every i bigger than or equal to 2. Then what will happen? That terms will be 0. Those terms will be 0. So, what is left is the first term f of s 1 minus.  Is that okay? In equation 3, I am putting s 2 equal to t 2, s 3 equal to t 3 and so on. All remaining terms will be 0 except the first one. So, first one will be f of s 1 minus f of t 1 into the length. So, that is x 1 minus x 0. So, that is the case. So, what is mod f of s 1 is less than or equal to? What is mod of f? So, mod of f t 1 into x 1 minus x 0 plus 2 epsilon. Is that okay? From here, this implies this. Is that okay? Mod of a minus b less than something. So, what is mod a less than? At triangle inequality again, you can add and subtract if you like. Now, look at this quantity. f of t 1 is the value at some point t 1, length of the interval. So, this is less than or equal to some number. f of t 1 is the value of the function at a point t 1 of your choice. You can take at f of t 1 to be a left end point a 1 a. So, f of a into the length. So, you can put maximum b minus a. This is the length of the sub interval. You can bind it by the total interval plus 2 epsilon. Is that okay? f of t 1, t 1 is a arbitrary point in the interval x i minus 1 to x i. So, let me take the arbitrary point as the left end point a. So, t 1 is equal to a x 1 minus x 0. That is the length of the sub interval. So, that is less than the length of the full interval. That is b minus a 2 epsilon. So, call this as some constant m. So, what is s 1? s 1 is an arbitrary point in the first part. So, what we have shown is the function is bounded in the interval x 0 to x 1. s is arbitrary. So, since s is arbitrary, s 1 is arbitrary in the first part. So, that is a 2 x 1. f is bounded in x 0. That is a 2 x 1. So, what we have shown is we have found a partition. Now, so how do I get the first one? By choosing s i equal to t i. I can do it for the other ones now. s i equal to t i everywhere for all i except 2. So, I will get boundedness in the second interval and so on. Similarly, other sub intervals. So, let me write. So, similarly f bounded in each one of x i minus 1 to x i for every i and that proves it. You can divide by that also. So, to be very precise, it should have been multiplied by this. So, 1 over of b minus a. Put that also if you like. Take it on the other side. This is a constant multiplying. That is what your question is. This multiplied by x 1 minus x 0. If I divide, it will be 1 over of this quantity. So, 1 over of, I should not say I write 1 b minus a. I should write it as something else. I think f of s 1 minus, that makes it smaller. There is a minor thing. I think from here, if you want to go, then you should, yes, that is a small h. I should, because this will not give you directly this. You have to divide by that. x 1 minus x 0. So, this is not correct. We should have x 1 minus x 0 multiplied by this is less than or equal to this quantity. So, we will have 1 over of x 1 minus x 0. Can I bind that with something? Yes, I think.