A circle of diameter $1$ is removed from a $2\times 3$ rectangle, as shown.  Which whole number is closest to the area of the shaded region?
[asy] fill((0,0)--(0,2)--(3,2)--(3,0)--cycle,gray); draw((0,0)--(0,2)--(3,2)--(3,0)--cycle,linewidth(1)); fill(circle((1,5/4),1/2),white); draw(circle((1,5/4),1/2),linewidth(1)); [/asy]
$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 5$
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 $5\rightarrow \boxed{\text{E}}$.