We are given: Suppose f is a real-valued function defined on the closed and bounded interval $I = [a, b] \subset \Bbb R$. And on the previous problem we proved that for each $\varepsilon > 0$, if there exists a subdivision $\delta$ of $I$ such that $S^+(f, ∆) − S_−(f, ∆) < \varepsilon$, then $f$ is integrable on $I$.
We're told to use the previous result to prove the current one. I'm thinking uniform continuity is the way to go, but am unsure how to approach it. Can anyone give me some guidance on what to do or how to approach this problem?