Problem:

Here's what I have so far.If is a non-negative, Riemann-integrable, uniformly continuous function on , prove that .

I want to try to prove that converges. Since is uniformly continuous, such that when .

Let be a partition of such that . Let on and let on . We know that:

Now I get stuck. I was thinking that since I know , I could put some restrictions on and , but I'm not sure how to do this. Am I on the right track? Regardless, can someone give me a hint as to the best way to proceed?