The rule for integration is shown below.
This is the symbol of integration.
This is included because you are integrating with respect to x.
C is the constant of integration. When you differentiate, constants disappear, so lots of functions have the same derivative. When you integrate, the constant is unknown, so you have to write +c at the end.
Consider this equation.
Putting this into the above formula shows us this:
Similar to differentiation, with an equation with many different terms of x, each separate one is integrated separately. For instance: