Integral

The process of finding integrals is called integration.
* Definite Integral: the integral of a real-valued function f(x) on [a,b] is denoted by: \int_a^b f(x) dx.
* Indefinite Integral (a.k.a. Antiderivative): \int f(x) dx represents a class of functions whose derivative f(x). 
In both, \int indicates the operation of the integral, the function f(x) is called the integrand. If limits on the domain of which the function is integrated are specified, we speak of a definite integral.
== Ways to Think about Integrals ==
* Area under the curve of a nonnegative integrable function
* Net area of an integrable function (not necessarily nonnegative, e.g. the integral of the sine function from zero to two pi has zero area).
* Inverse operation of derivative (antiderivative)
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== Categories of Non-Integrable Functions ==
The question: 'which functions are integrable?' Doesn't seem to have a straightforward answer? (at least, I haven't found it yet. It will also depend on which type of integral?)
* Non-bounded
* Non-monotonic?
* Non-measurable?
* etc. etc. 
== Types of Integrals ==
Riemann Integral
Lebesgue Integral
Rieman-Stieltjes
Darboux Integral