jmc

The area of the shaded region is the area of the circle subtracted from the area of the rectangle. The diameter of the circle is $1$, so the radius is $1/2$ and the area is $$(1/2{)}^2\pi =\pi /4.$$ The rectangle obviously has area $2\times 3=6$, so the area of the shaded region is $6-\pi /4$. This is closest to $5\to \boxed{5}$.