The integral operator is represented by the integral symbol and has four parts: the expression being integrated, the differential, a start value and an end value. Typically, the operator appears in an expression like this:
In plain language, this means take the integral of the function with respect to along range from to . Importantly, the differential “” expresses which variable is being integrated.
When a start and end value are included the integral is called a definite integral since the author is usually expressing that they want to calculate the result of the integral. When there is no start and end value the integral is called an indefinite integral. To read more about computing both definite and indefinite integrals see this page.
Type  Notation  

Definite Integral  \int_{a}^{b} f(x)dx 

Indefinite Integral  \int f(x)dx 