u substitution integration

1. Indefinite integrations:          An indefinite integration is the family of functions that have a given function as a common derivative. The indefinite integral of f(x) is written ∫ f(x) dx.2. Definite integrations:                If F(x) is the integral of function f(x) over the interval [a, b] ,i.e., ∫ f(x) dx = F(x) then the definite integral of function  f(x) over the interval [a, b] is denoted by `int_a^bf(x)dx` and is defined as `int_a^bf(x)dx`  = F(b) – F(a).                   Where 'a' is called the lower limit and b is called the upper limit of integration and the interval [a, b] is called of integration.Methods of integration:                        It is not possible to integrate each integral with help of the following methods but a large number of varieties of the problems can be solved by these methods so, we have the following methods of integration:                        1. Integration by substitution                        2. Integration by parts.                        3. Partial fractions