Remember old high school days?
the integral
is defined informally to be the net signed area of the region in the xy-plane bounded by the graph of ƒ, the x-axis, and the vertical lines x = a and x = b.
This cool PHP script, gets a diagram expression, start and end point for the variable x and calculates the integral of the given expression between start and end points. You'll also get a nice diagram with a graphical representation. You can increase the accuracy of the caclulation by choosing a smaller calculation step from the dropdown menu. Obviously the smaller the step is, the longer the calculation be.
Here is a sample output for f(x)=sqrt(x)*5
Try it here. The code is also downloadable from phpclasses.org.