• ### 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