Basic Analysis I — Real Analysis · Problem 5.3.6

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · fundamental-theorem-of-calculus

Problem

Suppose

F

and

G

are continuously differentiable functions defined on

[a,b]

such that

F'(x) = G'(x)

for all

x \in [a,b]

. Using the fundamental theorem of calculus, show that

F

and

G

differ by a constant. That is, show that there exists a

C \in \mathbb{R}

such that

F(x) - G(x) = C