Find the antiderivative, without the constant C. You can either do it in one step or separate the function into three terms.
The antiderivative of x^2 is x^3 / 3
The antiderivative of e^x is e^x
The antiderivative of -6 is -6x
Evaluate at 1
Evaluate at 0
Subtract the answer at 0 from the answer at 1.
Good luck!
Read this: Table of Integrals
All these should be in your textbook and/or class notes.