ABSTRACT
Wenowwill establish one of the most important results in all of mathematics, the fundamental theorem of calculus. To do so, we note that if f : [a, b] → R is bounded and integrable on [a, b], then it is integrable on every subinterval [a, u] ⊂ [a, b], and therefore the integral
∫ u a f (x) dx determines a function F (u)
defined on [a, b]. This function has nice properties, as the following theorem establishes.
