Basic Analysis I — Real Analysis · Problem 5.2.3

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · riemann-integrability

Problem

Let

f : [a,b] \to \mathbb{R}

be Riemann integrable, and

g : [a,b] \to \mathbb{R}

be such that

f(x) = g(x)

for all

x \in (a,b)

. Prove that

g

is Riemann integrable and that

\int_a^b g = \int_a^b f.