Exercise 1: For the following statements, say true or false. If true, provide a brief reason. If false, provide a counterexample. (a) If f and g are integrable on [a, b], and g(x) # 0 on [a, b], then f/g is integrable on [a, b]. (b) Suppose for all a, b e R, ƒ and g are integrable on [a, b]. If Sº f = L° g for all a, b, then f = g. (c) If f is integrable on [a, b], then F(x) = S* f(t) dt is continuous on [a, b]. (d) If ƒ is strictly increasing and integrable on [a, b], and a < c < b, then , f(t) dt < [, f(t) dt. (e) Suppose f and g are integrable on [a, b] and for all c e (a,b), S. f(t) dt < S g(t) dt. Then f(x) < g(x).

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