Riemann Sums Converging to an Integral
 
Maple 8 code: 
with(plots): with(student):
pic := n-> 
    [rightbox(x+sin(x)+3,x=0..2*Pi,2*n,
     tickmarks=[0,0])]:
display(seq(pic(n),n=1..20),insequence=true);
 
Comments: 
  1. This animation shows Riemann sums for a function, using n = 2, 4, 6, 8, ..., 40 subintervals.
  2. This animation will have to be slowed down for display on almost all computers.  The one above displays frames for varying times, the first and last frame being displayed for the longest times.