/sci/ - Science & Math

Why the fuck is the integral of f(t) on [a, b] equal to F(b) - F(a)?
My fucking lecturer didn't explain this shit at all.
Why anti derivatives? Why/how do they work and how are they related to this? how do derivatives even relate to this at all?
I don't get the logic at all.

Please tell me I'm not the only one who struggles with this shit.