Lower and Upper Sum

This worksheet shows the graph of a cubic funktion defined by f(x) = -0.5x3 + 2x2 – x + 1. The area enclosed by graph and x-axis is approximated by rectangles: [color=#1551b5]blue for lower sums[/color] and [color=#c51414]red for upper sums[/color]. The slider allows you to determine the number of rectangles used.

Move the points A and B to approximate the area between y-axis, graph, x-axis and root of the function. Change the value of n and watch how the difference between upper and lower sum changes. Can you explain your observations?