2.(a) Show that If f is continuous on [a,b] and c is any number in [a,b], then the function F(x) = f(t)dt is continuous on [a,b], differentiable on (a,b), and satisfies F'(x) = f(x) for all x in (a,b). (Hint: f(t)dt = f(t)dt + f(t)dt )