Definite+Integrals-+Fundamental+Theorem+of+Calculus+Parts+I+and+II

=The Fundamental Theorems of Calculus=

Well over 200 years ago, Isaac Newton and Gottfried Wilhelm von Leibniz discovered what has been called the most influential computational discovery in the history of mathematics: The connection between the Derivative and the Integral. This connection is shown mathematically as Parts One and Two of the Fundamental Theorem of Calculus.

//The Fundamental Theorem of Calculus, Part One//
This theorem states that the Derivative and the Integral are inverses of each other. They will cancel each other out (shown above), and for this reason the Integral is sometimes known as the "anti-derivative."

The Fundamental Theorem of Calculus, Part Two
This statement allows for definite integrals to be calculated without the tedious use of limits or the approximations involved with Riemann sums.