Area under the Curve

Use this applet to explore the differences between the Lower Sum, Upper Sum and the Area Under the Curve.
Use the input bar to type in your own function for f(x). Then adjust the start and end values as needed to fit your function (Usually between x-intercepts). Use the check boxes to show the lower sum, upper sum, or the area under the curve. Then adjust the number of rectangles. What do you notice about the lower and upper sums as the number of rectangles increases?