This applet is designed to help you understand two very important numerical methods of integration - the Trapezium Rule and the Mid-Ordinate Rule.
Varying A, B, C and D changes the curves. (Note that if you're in quadratic mode, A no longer is relevant, so clicking it will have no effect. Similarly, in linear mode A and B are not used.)
You can move the two integral limits by clicking and dragging the two yellow circles with your mouse.
Clicking on "Trapezium/Mid-Ordinate" flips between the two methods.

Clicking on "Strips +" or "Strips -" increases or reduces the number of strips taken between the two limits.
By playing around you should develop an insight into how the area between the curve and the x-axis is related to the value of the integral. You should also investigate whether the approximations are underestimates or overestimates, and how the error can be reduced. The error is given to you by comparing the numerical method with the exact integral (from algebraic calculus), rounded to 2 d.p.