This applet initially shows the function f(x)=x^2, and the area under the curve above the interval [a,b]. It starts with a=0 and b=2; the value of c is the shaded area, and the point (b,c) (a point on the antiderivative produced in the First Fundamental Theorem of Calculus) is plotted.
The purpose of this applet is to plot the antiderivative from FTC-1, even if you don't know a formula for it. You set the left and right limits on the plot in the obvious boxes; they are set initially to [-5,5]. Set "a" to be your lower limit of integration. The slider then moves "b" in increments of 0.1 units from the left limit of your plot to the right limit, tracing out the point (b,c) in red as it goes. These points (b,c) are on the graph y = F(x) from FTC-1, an antiderivative for f(x). Looking at the shape of the plot of red dots, you can enter a candidate formula for the antiderivative in the indicated box (initially this is set to the constant function y=0). This produces a dotted green plot that, if you are correct, will pass through all of the red dots.