Answer
$$\int_{0}^{1} x^{5} d x \leq \int_{0}^{1} x^{4} d x$$
$$
\int_{1}^{2} x^{4} d x \leq \int_{1}^{2} x^{5} d x
$$
Work Step by Step
Since $x^{5} \leq x^{4},$ for $x\in [0,1] $, then
$$\int_{0}^{1} x^{5} d x \leq \int_{0}^{1} x^{4} d x$$
and $x^{4} \leq x^{5}$ for $x \in[1,2]$, then
$$
\int_{1}^{2} x^{4} d x \leq \int_{1}^{2} x^{5} d x
$$