A company determines that the marginal profit P'(x) of producing and selling xth unit of a certain product is given by: P'(x) = 2x² - 2x + 25e^-0.5x . Find the total cost function P(x) and the initial profit is $150 due to fixed cost.

a. Set up the integral to find the total profit function. (2 pts)

b. Find the general total profit function (x) and use the given information (0, - 150) to find the valueC

c. Find P(40)