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In mathematics, the definite integral
is the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the lines x = a and x = b, such that area above the x-axis adds to the total, and that below the x-axis subtracts from the total.
The fundamental theorem of calculus establishes the relationship between indefinite and definite integrals and introduces a technique for evaluating definite integrals.
If the interval is infinite the definite integral is called an improper integral and defined by using appropriate limiting procedures. for example:
A constant, such pi, that may be defined by the integral of an algebraic function over an algebraic domain is known as a period.
The following is a list of the most common or interesting definite integrals. For a list of indefinite integrals see List of indefinite integrals.