Difference Between Lower and Upper Sum
The following applet compares the difference between the lower and upper sum in approximating the integral of a function.
Move the Slider to change the number of rectangles used to approximate the integral.

1. What happens to the difference between the upper and lower sum as the number of rectangles is increased?
2. Do the Upper sum and lower sum get closer to the value of the integral as the number of rectangles is increased?
3. What is the best approximation to the integral: The Upper sum, lower sum, or an average of the upper and lower sum?