Ok, I am starting a 2D sidescroller project in C++ and OpenGL. In any normal game using a low end graphics api, I would normally not draw anything that wasn't on the screen. However, I see that OpenGL has some functions that do that too. I was wondering whether it was worth it to cut off the parts not shown on my own? Or should I let OpenGL do it. The answer should be based on performance, because I want a high fps for a 2d game. And if I let OpenGL do it, how? Thank you in advance!

u should always perform gross culling yourself.
eg send as little data to op3engl as possible

Listen to zedzeek. While OpenGL won't draw anything not on the screen, it still requires an API call which can cumulatively get expensive, especially if the calls are essentially being ignored anyway.