Riemann integrable, function

Suppose that is a Riemann integrable on and for all . Prove that is Riemann integrable on .

Relevant Theorems & Definitions

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

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.

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

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