5. Let f : [a, b)R and f(r) 2 0 for all r e la, b V(a) If f is integrable, show that f(z)dr 2 0. (b) If f contimuous and f(z)dr 0 show that f (x) = 0 for all z E (a, b). (c) Give an example of an integrable function f on (a, b such that f(r) 2 0 for all zE (a, b) and S(z)dr 0 but f (xo) #0 for some ro E [a, b). !3!

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