Suppose we want to find the area under the function $f\left(x\right) = 2^{x}$ on the interval $1 ≤ x ≤ 3$. 

1. Sketch a graph of the curve shading the area of the region you are to find.

2. If left-endpoint rectangles are used will the estimate be too low or too high. Justify your answer.

   Answer (b):

   Too low, as rectangles will be under the curve.

3. If you used right-endpoint rectangles to estimate the area, will that estimate be too low or too high. Justify your answer.

   Answer (c):

   Too high, as rectangles will be above the curve.

4. Use your program to find an estimate using $20$ left- and right-endpoint rectangles.

   Answer (d):

   $\text{Left}=8.360$, $\text{Right}=8.960$