Answer
$$0$$
Work Step by Step
\begin{aligned} \int_{-1}^{1} \frac{d x}{x^{0.2}} &=\int_{-1}^{0} \frac{d x}{x^{0.2}}+\int_{0}^{1} \frac{d x}{x^{0.2}} \\ &=\lim _{R \rightarrow 0^{-}} \int_{-1}^{R} \frac{d x}{x^{0.2}}+\lim _{R \rightarrow 0^{+}} \int_{R}^{1} \frac{d x}{x^{0.2}} \\ &=\left.\lim _{R \rightarrow 0^{-}} \frac{x^{0.8}}{0.8}\right|_{-1} ^{R}+\left.\lim _{R \rightarrow 0^{+}} \frac{x^{0.8}}{0.8}\right|_{R} ^{1} \\ &=\lim _{R \rightarrow 0^{-}} \frac{R^{0.8}-1}{0.8}+\lim _{R \rightarrow 0^{+}} \frac{1-R^{0.8}}{0.8} \\ &=-\frac{5}{4}+\frac{5}{4}\\
&=0 \end{aligned}
