They are inverses - up to a constant. Your f(x) and the result of your integration differ by a constant (1, in this case). That is, if you add 1 to the result of your integration, you will get the function with which you started.
Hey what's going on here. I thought if you take the derivative of a function, then integrate that derivative, you get the original function back.
But when I perform this routine on the function below I get a different function from the original. I'd appreciate it if someone could point out where I've gone astray. Thanks.