Introduction to Area Under a Curve

In this applet from the GeoGebra Calculus Applets Project, you enter a function and position endpoints to see what the value of the integral is.

Accumulated Rate of Change and Antiderivatives

This applet from the Flash Mathlets collection by Barbara Kaskosz includes graphs of a bunch of sample rate of change functions. For each, as you drag a slider, you see what the associated population (i.e., antiderivative) would look like. You can also input your own rate of change function and initial condition. What's more, you can draw your own  function, specify an initial condition, draw what you think the associated antiderivative would look like, and then check your antiderivative by moving the slider to see the applet draw the antiderivative.

Definite Integral as an Area Accumulator

This clear, elegant applet from the Flash Mathlets collection by Barbara Kaskosz shows the integral as an area accumulator for a few simple functions.