## Mathematical Analysis## Integral Calculus |

## What is the Fundamental Theorem of the Calculus? |

The Fundamental Theorem of the Calculus is the connection (or, more accurately, the bridge) between the integral and the derivative; in other words, it is another way of finding the area under a curve (see above) by evaluating the integral. In particular, if *F*(*x*) is a function whose derivative is *f*(*x*), then the area under the graph of *y* = *f*(*x*) between the points *a* and *b* is equal to *F*(*b*) - *F*(*a*). This is seen as the following notations:

The number *F(b)* - *F(a)* is also denoted by

Thus,