So I have to review this stupid old shit for no reason.

This problem should be simple as fuck. With power rule I already know deriv is 2t -1.
f(t)=t² - t

But I have to find the deriv using
f(t+h)-f(t)
h
So I plug shit in:
(t+h)² - (t+h) - (t² - t)
h

Simplify:
t² + 2th + h² - t - h - t² + t
h

Simplify more:
2th + h² - h
h

Divide all by h and you get:
2t + h - 1

Why the hell is there still an h in here? Am I totally missing something?

because you forgot that all of this stuff is under the limit as h approaches 0
you've done it all correctly though. Since h -> 0, the expression just becomes 2t-1

I knew it would be something stupid like that. Thank you, I waaay overthought this.