Basic Analysis I — Real Analysis · Problem 5.1.2

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · riemann-integral-definition

Problem

Let

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

be defined by

f(x) := x

. Show that

f \in \mathcal{R}([0,1])

and compute

\int_0^1 f

using the definition of the integral (but feel free to use the propositions of this section).