This is one of the most powerful geogebra activities I have used. Students typically have a difficult time developing a way of thinking about how the definite integral [math] \int_{a}^{x}{f(t)dt}=F(x) [/math] can itself be a function. This applet helps students to see this relation as a Riemann sum type of limit.
One fun extension to this discussion is to ask what will happen if one slides the left limit (a) to the right or left. Then ask about moving the right limit (b). Allow a full discussion before showing the results. Have students explain the results.
To use: set "a" and "b" to the desired upper and lower bounds for the overall sum. Start with a small "n" and ask what will happen to the accumulated values as I increase "t" (the percentage of the distance across the interval [a,b]).
