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                                      Michael Lee's Mathematics and Physics

The Fundamental Theorem of Calculus is as follows.    Notice how the area under the function f(x) is another function called F(x); it is the antiderivative of the original function.




 I use the letter A to represent the area under the function f(x) as opposed to S-s shown above in the animation.

The width (w) of the "bars" that compose the definite integral is shown below.

If the function f(x) is a continuous function between points a and b then,




Here is another example...