Suppose that is Riemann integrable on and is bounded on . Prove that is Riemann integrable on .

Relevant Theorems/Definitions

Definition - Riemann integrable - if upper integral of = lower integral of .

Theorem - Riemann integrable iff for each a partition of such that .

Theorem - Riemann integrable iff such that a partition of such that marked refinements of , , where .

Theorem - Let be a continuous function on . Then is Riemann integrable on .

etc.

I don't know how to start this problem. I need a head start on where to go with this one. Thanks in advance.