english: Since $ {c_1}$ is between $ {.9}$ and $ {1}$, and we’re multiplying $ {f(c_1)}$ by $ {.1}$, that could be the same calculation we would do if we were approximating the area under $ {f(x)}$ from $ {0}$ to $ {1}$ with $ {10}$ rectangles: each rectangle has width $ {.1}$, so that’s why we multiply by $ {.1}$.
non_english: うぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅうぐぅぅうぐぅうぐぅぐ～ぐ～ぐ～。。。。