The integral operator is represented the by the integral symbol, a start and end value that describe the range of the integral, the expression being integrated, and finally, the differential which indicates which variable is being integrated with respect to. For example, the integral operator is commonly used as shown below.
In plain language, this means take the integral of the function on the range from to with repect to . For multi-variable functions the differential indicates which variable is being integrated over.
The integral operator is used to describe definite integrals and indefinite integrals. The difference in notation between the two is that the definite integral has start and end values and the indefinite form does not.