5. Given f [a, b] R and g [a,b] - R are both bounded with g(x) f(x) for all xe [a, b]. Let P be any partition of [a, b]. Prove that U(g, P) U(f, P). 6. Let f [1,5] R with f(x) = = 2x for 1 x < 3, f(3) = 8 and f(x) = -3 for 3 < x < 5. a. Use the A-R theorem to prove directly that f is integrable. b. Use the A-R theorem to calculate f