Nice catch.

Your correction appears to me to be correct. You need to evaluate the integral at x=1, and x=0. (Fundamental theorem of calculus) F(1) - F(0).

This would give you,

I think this is an exact solution which would mean the upper bound on the error would be zero or any positive number for that matter, but I hardly suspect this is what your question is asking us for. I am not sure how to proceed from here.

Taylor Polynomials provide an error equation, which you could use to find the upper bound of the error. However, we are going for infinite terms so the power series becomes exact.

Please let me know if/when you figure out this solution.