Assume that f is continuous on [a, b] and let A be the area function for f with left endpoint a. Let m^* and M^* be the absolute minimum and maximum values of f on [a, b], respectively.

a. Prove that m^*(x - a) ≤ A(x) ≤ M^* (x - a) for all x in [a, b]. Use this result and the Squeeze Theorem to show that A is continuous from the right at x = a.

b. Prove that m^*(b - x) ≤ A(b) - A(x) ≤ M^*(b - x) for all x in [a, b]. Use this result to show that A is continuous from the left at x = b.