
Antiderivative
An antiderivative of a function f (x) is a function F(x) such that F'(x) = f (x).

Definite Integral
The limit approached by the nth upper and lower Riemann sums as n→∞.

Integrable
The property that the definite integral of a function exists; that is, the upper and lower Riemann sums converge to the same value as the size of the approximating rectangles shrinks to zero.

Riemann Sum
The sum of areas of rectangles approximating the area under the graph of a function; examples include the upper and lower Riemann sums.

Fundamental Theorem of Calculus
The relationship between differentiation and integration:
F'(x)dx = F(b)  F(a) f (t)dt = f (x)

Lower Riemann Sum
An approximation to the area below the graph of a function, equal to the total area of a number of thin rectangles inscribed in the region below the graph.

Upper Riemann Sum
An approximation to the area below the graph of a function, equal to the total area of a number of thin rectangles containing the region below the graph.

Telescoping Limits
The following property of the definite integral:
f (x)dx + f (x)dx = f (x)dx