- #1

bonfire09

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## Homework Statement

Prove the function ##f(x):[2,4]\rightarrow\mathbb{R}## defined by ##f(x) =\begin{cases} x, & \text{if }2\leq x\leq 3 \\2, & \text{if } 3<x\leq 4 \end{cases}## is Riemann Integrable

## Homework Equations

A function ##f:[a,b]\rightarrow\mathbb{R}## is integrable iff for each positive number ##\epsilon## there is a partition ##P## of the interval ##[a,b]## such that ##U(f,P)-L(f,P)<\epsilon##.

## The Attempt at a Solution

I've been struggling with this problem for a while and I am having a tough time figuring out what my partition should be? I know the function is increasing on ##2\leq x\leq 3## and is constant on ##3<x\leq 4##. And also what is the best way of figuring out the partition?