Answer
the integral diverges
Work Step by Step
$\int{\frac{dx}{x^{2}}}$ = $-\frac{1}{x}+C$
$\int_{-1}^{0}{\frac{dx}{x^{2}}}$ = $\lim\limits_{R \to {0^{-}}}$$\int_{-1}^{R}{\frac{dx}{x^{2}}}$ = $\lim\limits_{R \to {0^{-}}}$$-\frac{1}{x}|_{-1}^{R}$ = $\lim\limits_{R \to {0^{-}}}$$(-\frac{1}{R}+1)$ = $1-\lim\limits_{R \to {0^{-}}}$$\frac{1}{R}$ =$\infty$
$\int_{0}^{1}{\frac{dx}{x^{2}}}$ = $\lim\limits_{R \to {0^{+}}}$$\int_{R}^{1}{\frac{dx}{x^{2}}}$ = $\lim\limits_{R \to {0^{+}}}$$-\frac{1}{x}|_{R}^{1}$ = $\lim\limits_{R \to {0^{+}}}$$(-1+\frac{1}{R})$ = $-1+\lim\limits_{R \to {0^{+}}}$$\frac{1}{R}$ =$\infty$
