Early in the 14th century, a group of scholars in Oxford, England, explored how to find the accumulated distance from knowledge of the velocity. In 1638, Galileo used their ideas to explain the motion of falling bodies and justify his claim that the earth circles the sun. Later in that century, Isaac Newton studied these accumulation functions, and in 1666, discovered a remarkable insight that connected accumulation functions to what he already knew about derivatives. If there was one moment when calculus was born, this was it.

Today, what we call the

*integral*calculus or

*integration*has two distinct interpretations. We begin this chapter by looking at integration as accumulation. but is also can be viewed as reversing the process of differentiation, what we call

*antidifferentiation*. Newton's insight, that these two are connected, is what is called the Fundamental Theorem of Calculus. (Taken from an excerpt in the fifth edition of the Finney, Demana, Waits, Kennedy, and Bressoud textbook

*Calculus - Graphical, Numerical, Algebraic*.)