Answer
Diverges
Work Step by Step
\begin{aligned}
\int_{1}^{2} \frac{d x}{(x-1)^{2}} &=\lim _{R \rightarrow 1} \int_{R}^{2} \frac{d x}{(x-1)^{2}} \\
&=\lim _{R \rightarrow 1}\left.\frac{(x-1)^{-1}}{(-1)}\right|_{R} ^{2} \\ &=\lim _{R \rightarrow 1}\frac{1}{(R-1)}-1 \\
&=\infty\end{aligned}
The integral diverges.
