integration and differentiation

I have read different topics of integration and differentiation, i mean different ways to integrate or differentiate. The problem is i don't understand that, is there any specific way to solve a particular problem. For example we know how to add, when talking of integration and differentiation no one tells that to integrate of differentiate a function we should follow these rule. although looking at the function type we can up to some extent decide the procedure to use, still often i personally encounter such problem that i cannot solve without taking help from outside. So please can anyone tell me are there any specific rule that if we follow we can solve any problem of integration or differentiation, or its just practice and experience that can help.