Answer
$$1$$
Work Step by Step
Determine interval over which to integrate
We'll be integrating with respect to $y$ over the interval $1 \leq y \leq \leq 2$
$$
\text{Note that we're merging with y thus it's the right curve minus the left curve.}\\
\begin{array}{c}
\int_{1}^{2} y-\frac{1}{y^{2}} d y \\
{\left[\frac{y^{2}}{2}+\frac{1}{y}\right]_{1}^{2}} \\
{\left[\frac{2^{2}}{2}+\frac{1}{2}\right]-\left[\frac{1^{2}}{2}+\frac{1}{1}\right]} \\
{\left[\frac{4}{2}+\frac{1}{2}\right]-\left[\frac{1}{2}+\frac{2}{2}\right]} \\
\frac{5}{2}-\frac{3}{2}=\frac{2}{2}=1
\end{array}
$$