Problem:
Graphically investigate the function

with x between 0 and 2 pi and for various values of a between 0 and 2 pi.

Visualization:

The following is code to construct an animation for such an investigation using the program Maple.

> with(plots):
> F:=x->int(sin(t),t=a..x);

> animate({sin(x),F(x)}, x=0..2*Pi, a=0..2*Pi, frames=50, color=blue);

[Press here to see animation]

The animation shows the graph of y = sin(x), the x-axis, the y-axis and the graphs of y= F(x) as a varies from 0 to 2 pi.