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