**Problem Statement: **Let . Prove is Riemann Integrable on and .

**Proof:** First note that each is continuous on and since is a sum of continuous functions it follows that is continuous on . Furthermore, since is a compact set it follows that this convergence is uniform. Since we have uniform convergence we get the following:

**Reflection:** At first glance this problem scared me. But, after being reminded by Suz that convergence of a sum to a function on a compact set gives us uniform convergence my life was made easier. This is another one of those handy facts to remember.

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