jmc

Each diameter of a circle is 2 units. The rectangle is 2 diameters by 1 diameter, or 4 units by 2 units. Its area is thus 8 square units. Each circle has an area of $1^2\pi =\pi$ square units, so the two circles have a combined area of $2\pi$ square units. The total shaded area is that of the rectangle minus that of the excluded circles, or $\boxed{8-2\pi }$ square units.