CPM Homework Help : PC Problem 6-13

Consider the function $f(x)=-\frac{1}{2}\left(x−1\right)^2+7$ for $1\le x\le4$ .

Write the sum to find the area under the curve using left-hand endpoints and rectangles with widths of $1$ . Since you are not using a calculator, be sure you set up your sum to include all of the factors. You do not need to actually calculate the sum.
Hint (a):
$f(1)+f(2)+f(3)$
Write the sum using sigma notation.
Hint (b):
$\displaystyle \sum_{k=1}^{3}(-\frac{1}{2}(??)^2 +7)$

Compute without a calculator