You are trying to find the area $A\left(f, 1 ≤ x ≤ 2\right)$ for $f\left(x\right)=-x^2+6$.

1. Use $4$ rectangles to find the upper and lower bounds of the area.

   Upper Bound Hint (a):

   Upper Bound means that the rectangles will give an over estimate.

   

   Lower Bound Hint (a):

   Lower Bound means that the rectangles will give an under estimate.

   

2. Express the sum of the lower bound using sigma notation.

   Partial Answer (b):

   $.25\displaystyle\sum_{k=1}^{4}-(\text{find this expression})^{2}+6$