# If f is a bounded function and Riemann integrable on a subset [a',b] of [a,b], prove that f is integrable on [a,b].

Let f : [a,b] $$\to$$ $$\mathbb{R}$$ be a bounded function such that f $$\epsilon$$ $$\mathcal{R}$$[a',b] (ie: f is Riemann integrable) for every a' $$\epsilon$$ (a,b).

Prove that f $$\epsilon$$ $$\mathcal{R}$$ [a,b].

I'm a little stuck as to how to start this one. It seems simple but the professor has it weighted kind of heavily in the assignment.