## The Indefinite Integral

An indefinite integral is quite simply an 'Area Function'. It is a function of some variable, say x, which when taken between two x values, returns the area under the curve between those x values.

The diagram shows the graph of
$y=4-x^2$
.
The indefinite intefgral is
$\int x^2 dx = \frac{x^3}{3}+c$
.
The constant
$c$
is called the constant of integration and reflects the fact that any constant differentiates to give zero. Remember that integration and differentiation and differentiation sre inverse processes.