Basic Analysis I — Real Analysis · Problem 5.2.1

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · linearity-of-integral

Problem

Finish the proof of the first part of Proposition 5.2.4. Let ff be in R([a,b])\mathcal{R}([a,b]). Prove that −f-f is in R([a,b])\mathcal{R}([a,b]) and ∫ab−f(x) dx=−∫abf(x) dx.\int_a^b -f(x)\,dx = -\int_a^b f(x)\,dx.

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