1. INTEGRALS (a) Let f: [a, b] →→ R be a Riemann integrable function and let c be a positive constant. Prove that cf is Riemann integrable and that •Sf(x)dr. (b) Let f: [a, b] → R be a Riemann integrable function. Prove that -f is Riemann integrable and that fe- f(x) dx = is continuous. = c. [₁-f(x) dx = f(x)dx. (c) Let f: [a, b] →→ R be a (bounded) Riemann integrable function. Show that the function g: [a, b] → R defined by g(x) = f* f a f(t)dt

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