Real Analysis : Integrability

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Prove that if f : [a,b] ----> R is a bounded function that is continuous at all but finitely many points, then f is integrable over [a,b].

Proof.
Without loss of generality, we assume that f is continuous and bounded over the interval [a, b] except at point , we will prove that f is Riemann integrable over
[a, b].
We know that f is bounded by some number M over the interval [a, ...