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suppose that f is riemann integrable on [a,b] and f(x) >=0 for all x a) prove...

suppose that f is riemann integrable on [a,b] and f(x) >=0 for all x

a) prove that integral from a to b of f(x) dx >= 0

b) prove that if integral from a to b of f(x) dx = 0 and f is continous the f(x) =0 for all x in [a,b]

c) Find a counterexample which shows that the conclusion of part b may not hold if the hipothesis of continuity is removed

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