Let f [a, b] R be a continuous function. Show that for any c d such...

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Let f [a, b] R be a continuous function. Show that for any c d such that [c, d] C [a, b], there exists = [c, d] such that 1 rd () = - C d f(x) dr. Use this to prove that if F(x) = * (t) dt, a (2) (3) then F'(x) = f(x), V x [a, b]. (4) Let f [a, b] R be a continuous function. Show that for any c d such that [c, d] C [a, b], there exists = [c, d] such that 1 rd () = - C d f(x) dr. Use this to prove that if F(x) = * (t) dt, a (2) (3) then F'(x) = f(x), V x [a, b]. (4)