Question: Let f : Ja, b] - R be Riemann integrable (and in particular, bounded on [a, b]). For x E [a, b], let F(x) =

Let f : Ja, b] - R be Riemann integrable (and in particular, bounded on [a, b]). For x E [a, b], let F(x) = So f(t) dt. (i) Prove that F is continuous on [a, b]. (ii) If f is continuous at Co, prove that F is differentiable at co, and F'(x0) = f (x0)

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