Answer
$0\leq \int_{0}^{1}x^{3}~dx \leq 1$
Work Step by Step
From the definite integral $\int_{0}^{1}x^{3}~dx$, $x$ is between $0$ and $1$.
Frame the integrand $x^{3}$.
$0 \leq x \leq 1$
Raise to the power of $3$ all sides of the inequality:
$0^{3} \leq x^{3} \leq 1^{3}$
$0\leq x^{3} \leq 1$
Now using the property $8$ it follows:
$0(1-0) \leq \int_{0}^{1}x^{3}~dx \leq 1(1-0)$
$0\leq \int_{0}^{1}x^{3}~dx \leq 1$