Integration is to derivation as a plus is to a minus. That means that just like a minus reverses what a plus does, and vice versa, integration reverses what derivation does, and vice versa. Another way of putting it is that integration is finding the anti-derivative.
Now that you know this, you have also learned a method to check that your integrals are correct: After integrating, you can differentiate your answer to see whether you get the original expression that you integrated (called the integrand, the expression between the integral sign and ).
Below is an overview of the integrals of several known and important functions. You will be expected to know these integral rules by heart. I recommend that you memorize them to learn them well, and that you always write down the proper formula before applying it when solving exercises.