Mathematics

Problem

Consider the definite integral

I=\int_{-2}^{1}\bigl(x^{3}-4x^{2}+2\bigr)\,dx.

Answer the questions below. a. (i) Determine an antiderivative

F(x)

of the integrand. b. (ii) Hence calculate the exact value of

I

. Show all steps clearly. c. (iii) Comment on the sign of your answer and interpret what it indicates about the area represented by the integral.