# Integral Function

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An Integral Function is a range function that is an area function for some real-valued function.

**Counter-Example(s):****See:**Numeric Integration Task, Infinitesimal Number, Differentiation, Calculus, Antiderivative.

## References

### 2011

- (Wikipedia, 2011) ⇒ http://en.wikipedia.org/wiki/Integral
- Given a function
*ƒ*of a real variable [math]x[/math] and an interval [*a*,*b*] of the real line, the**definite integral**[math]\int_a^b f(x)\,dx[/math] is defined informally to be the net signed area of the region in the*xy*-plane bounded by the graph of*ƒ*, the*x*-axis, and the vertical lines*x*= [math]a[/math] and*x*=*b*. The term*integral*may also refer to the notion of antiderivative, a function [math]F[/math] whose derivative is the given function*ƒ*. In this case, it is called an*indefinite integral*, while the integrals discussed in this article are termed*definite integrals*. Some authors maintain a distinction between antiderivatives and indefinite integrals.

- Given a function