A function f on [a, b] is called a step function if there exists a partition P = {a = u0 < u1 < ··· < cm = b} of [a, b] such that f is constant on each interval (uj−1, uj ), say f(x) = cj for x in (uj−1, uj ). (a) Show that a step function f is integrable and evaluate " b a f.