Example 2. Compare the integrals $I_{1}=\int_{0}^{1} x d x$ and $I_{2}=\int_{0}^{1} x^{3} d x$, without calculating them
Solution. Since in the interval $(0 ; 1)$ we have $x>x^{3}$, then $\int_{0}^{1} x d x>$ $>\int_{0}^{1} x^{3} d x$

Answer. $I_{1}>I_{2}$