Let f.g: [a, b] + R be a Riemann integrable functions and define F(a) = | s()dt. G(x) = | gt) dt, va € (a, b). E a) Prove that if f(t) = g(t) for all t e (a, b), then F(x) < G(x) for all x € [a, b]. (b) Is it true that if F(x) < G(x) for all x € [a, b], then f(t) = g(t) for all t € [a, b]?
