(4) Prove that if n > m >0 then sin t dt m Hence show that dt exists. (5) (*) Suppose that g is continuous on a, b and that f is differ- entiable on (a, b) and its derivative is continuous on [a, b) with f'(t) > 0 for t E [a, b). Prove that for some & E a, b we can write f(t)g(t)dt = f(a) / g(t)dt + f(b) g(t) dt. E Hint: Integration by parts will help