In multidimensional space it may be partially generalized to surface integrals on over manifolds in the form of the generalized Stokes' theorem.  
The strongest form of this lemma is implicit in the Henstock-Kurzweil method, which applies gauge summations to all forms of the inverse relationship it implies.  It may be relaxed to Lebesgue's theorem for locally continuous curves.  In multidimensional space it may be partially generalized to surface integrals on over manifolds in the form of the generalized Stokes' theorem.  FTP, name this mathematical theorem that states that the integral of the derivative of function on an interval is equal to the change in the function on the interval.
The strongest form of this lemma is implicit in the Henstock-Kurzweil method, which applies gauge summations to all forms of the inverse relationship it implies.  
first fundamental theorem of calculus