### Home > PC > Chapter 2 > Lesson 2.3.5 > Problem2-132

2-132.

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 means that the rectangles will give an over estimate.

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

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

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