Chapter 6.1, Problem 69E

Another look at the Fundamental Theorem

69. Suppose that f and g have continuous derivatives on an interval [a, b]. Prove that if f(a) = g(a) and f(b) = g(b), then ${\displaystyle {\int }_a^b{f}^{\prime }(x)dx={\displaystyle {\int }_a^b{g}^{\prime }(x)dx}}$.