## Calculus (3rd Edition)

$$\int_{0}^{1} x^{5} d x \leq \int_{0}^{1} x^{4} d x$$ $$\int_{1}^{2} x^{4} d x \leq \int_{1}^{2} x^{5} d x$$
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 $$\int_{1}^{2} x^{4} d x \leq \int_{1}^{2} x^{5} d x$$