Just count up the area of the 8 rectangles. That is basically all it is.
Since you're starting at the left side of the rectangles, the height of the first rectangle is
\(\displaystyle \frac{-(3)^{2}}{4}+2(3)=\frac{15}{4}\)
The height of the second is \(\displaystyle \frac{-(3.5)^{2}}{4}+2(3.5)=3.9375\)
and so on. The last one will use x=6.5
The width of each rectangle is 1/2. Find the 8 heights, add them up, multiply the sum by 1/2.
There's your area.
