Integral from 3 to 6:: d/dt(4+3t^4)^(1/2)dt

this is an integral of a derivative, so what it becomes is:

∫ d/dt (4 + 3t^4)^(1/2) dt = (4 + 3t^4)^(1/2)

integrals of derivatives cancel each other out.

so all you have to do is evaluate it at 6 and 3 and then subtract

This is the integral of a derivative!
Do you understand anything about either? It sure doesn't look like it .....