A firm's marginal profit P as a function of its total cost C is given by dp dc = -100 (C - 5)². Find P(C), if P(95) = 45.

a) (P(C) = -100(C - 5)² + 45)
b) (P(C) = -100(C + 5)² + 45)
c) (P(C) = -100(C - 5)² - 45)
d) (P(C) = 100(C + 5)² + 45)