Answer
$$
\int_{0}^{1}\left(5-6 x^{2}\right) d x=3.
$$
Work Step by Step
$$
\begin{aligned}
\int_{0}^{1}\left(5-6 x^{2}\right) d x&=\int_{0}^{1} 5 d x-6 \int_{0}^{1} x^{2} d x\\
&\,\,\,\,\,\,\,\,\,\,\, \text{since} [\int_{0}^{1} x^{2} d x=\frac{1}{3}] , \text {then}\\
&=5(1-0)-6\left(\frac{1}{3}\right) \\
&=5-2\\
&=3.
\end{aligned}
$$
