Solve an Integral in Java

Take a look at JScience

The Apache Commons Math library contains, in the Numerical Analysis section, four different numerical integrators:

• Romberg's method
• Simpson's method
• trapezoid method
• Legendre-Gauss method

The Wikipedia article on Numerical Integration has a section on methods for one-dimensional integrals.

You should have no problem implementing the "trapezoidal" or "rectangle" rule.