Prove that f must have at least one zero in the interval a

Question

Question: (a) Show that the function f is continuous for all values of x in the interval [a, b] and

(b) prove that f must have at least one zero in the interval (a, b) by showing that f(a) and f(b) have opposite signs.

f(x) = x³ - 2x² + 3x + 2; a = -1, b = 1