$\begin{aligned} I &=\int_{1}^{3}\left|1-x^{4}\right| d x \\ I &=\int_{1}^{3}-\left(1-x^{4}\right) d x \quad\left(:-|x|=\left\{\begin{array}{ll}x, & x \geq 0 \\ -x, & x < 0\end{array}\right)\right.\\ I &=\int_{1}^{3}\left(x^{4}-1\right) d x \Rightarrow I=\left[\frac{x^{5}}{5}-x\right]_{1}^{3} \\ I &=\left(\frac{3^{5}}{5}-3\right)-\left(\frac{1^{5}}{5}-1\right) \Rightarrow I=\frac{232}{5} \end{aligned}$