What is the area of the region bounded by the line $x = \frac{y - 1}{2}$, the $y$-axis and the lines $y = 1$ and $y = 5$?

Explanation

1. 01

   The region lies between the curve and the $y$-axis, so integrate along $y$: $\int_1^{5} \frac{y - 1}{2}\,dy$.

2. 02

   $\frac{1}{2}\left[\frac{y^{2}}{2} - y\right]_1^{5} = \frac{1}{2}\left(\frac{15}{2} + \frac{1}{2}\right) = 4$ square units.