Taylor Expansion for Numerical Integration

Hey,

I'm looking for the error of the Trapezoidal method applied to the integral

The actual value of this integral in . Applying the trapezoidal method to the integral results for a small step size results in: . (I've checked this result and for small h, this is approximately equal to . (to precision above 5 decimal places in MATLAB))

So now I have to check the error of the method, which in general, for an integral is .

So I'm having trouble finding the taylor expansion of , but i know the coefficent of the h^2 term should be .

Thanks!!