Chapter 5 - Section 5.2 - The Definite Integral - 5.2 Exercises - Page 390: 43

$\int_{0}^{1}(5-6x^2)~dx = 3$

We can evaluate the integral using properties of integrals: $\int_{0}^{1}(5-6x^2)~dx$ $= \int_{0}^{1}5~dx - \int_{0}^{1}6x^2~dx$ $= \int_{0}^{1}5~dx - 6\int_{0}^{1}x^2~dx$ $= 5(1-0) -6(\frac{1}{3})$ $= 3$