Integrals: Boundaries and Infinity

(a)Let f:[a,b] ---R be continuous and f(x)>= 0 for all x an element of [a,b]. prove that if the integral between the boundaries b and a of f(x) dx =0 then f(x) =0 for all x an element of [a,b]

(b)Prove that the integral between infinity and 0 of e^-st .sinat dt = a/s^2 + a^2

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...e the minimum and maximum values of f on (a,b), respectively.

m<=f(x)<=M, then and given that . So,