I have a TI-89, but I'm not an expert.
If your teacher is going to be that cantankerous about it, I say lie to her. Say you disabled them, but really just define X, Y, Z, A, B, etc. to values that will screw up the functions and make it report 0 or some other nonsense number. Even if you backup the ROM on your computer, it seems like it'd be unnecessarily destructive to override the built in functions.
Prove your merit by also writing down every single step to your integrations and derivations so she knows that you are indeed working it out on your own. Explain to her that you got the TI-89 intending it to last a while, and that you can't afford to pick up an 84/83 right now. If she still complains, talk to your school board or principal about it. It's not worth the potential damage to your calculator, and Teachers are not able to get away with that crap anymore. As it should be.