Editing Integral (section)

== Terminology and notation ==
In general, the integral of a [[real-valued function]] {{Math|1=''f''(''x'')}} with respect to a real variable {{Math|1=''x''}} on an interval {{Math|1=[''a'', ''b'']}} is written as
:<math>\int_{a}^{b} f(x) \,dx.</math>
The integral sign {{Math|∫}} represents integration. The symbol {{Math|''dx''}}, called the [[Differential (infinitesimal)|differential]] of the variable {{Math|1=''x''}}, indicates that the variable of integration is {{Math|1=''x''}}.  The function {{Math|1=''f''(''x'')}} is called the ''integrand'', the points {{Math|1=''a''}} and {{Math|1=''b''}} are called the limits (or bounds) of integration, and the integral is said to be over the interval {{Math|1=[''a'', ''b'']}}, called the interval of integration.<ref name=":1">{{Harvnb|Apostol|1967|p=74}}.</ref> 
A function is said to be {{em|integrable}}{{anchor|Integrable|Integrable function}} if its integral over its domain is finite. If limits are specified, the integral is called a definite integral.

When the limits are omitted, as in

: <math>\int f(x) \,dx,</math>

the integral is called an indefinite integral, which represents a class of functions (the [[antiderivative]]) whose derivative is the integrand.<ref>{{Harvnb|Anton|Bivens|Davis|2016|p=259}}.</ref> The [[fundamental theorem of calculus]] relates the evaluation of definite integrals to indefinite integrals. There are several extensions of the notation for integrals to encompass integration on unbounded domains and/or in multiple dimensions (see later sections of this article).

In advanced settings, it is not uncommon to leave out {{Math|''dx''}} when only the simple [[Riemann integral]] is being used, or the exact type of integral is immaterial. For instance, one might write <math display="inline">\int_a^b (c_1f+c_2g) = c_1\int_a^b f + c_2\int_a^b g </math> to express the linearity of the integral, a property shared by the Riemann integral and all generalizations thereof.<ref>{{Harvnb|Apostol|1967|p=69}}.</ref>