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 .
The indefinite intefgral is .
The constant 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.
See also The Definite Integral.