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
n
th 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.
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

