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.


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