Basic Analysis I — Real Analysis · Problem 5.1.9

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · riemann-integrability

Problem

Suppose

f : [0,1] \to \mathbb{R}

and

g : [0,1] \to \mathbb{R}

are such that for all

x \in (0,1]

, we have

f(x) = g(x)

. Suppose

f

is Riemann integrable. Prove

g

is Riemann integrable and

\int_0^1 f = \int_0^1 g