Trigonometric substitution problem

The initial problem is: http://www.wolframalpha.com/input/?i=integrate(sqrt(x^2+-+1)%2Fx%2C+x%2C1%2C2)

My problem is not in the substitution part but rather on the limits of integration. I tried "an easy way out" which is to just use => instead of = signs and not put limits of integration and then just turn the variables into x variables (initial variables) and use the initial limits of integration but the problem I am having is from this step:

integral of (tan^2 (theta) (dtheta)) = tan(theta) - (theta) + C = sqrt(x^2 - 1) - arcsec(x) and when I try to find the value for the final answer:

sqrt(2^2 - 1) - **arcsec(2)** - 0 + **arcsec(1)**

both bold parts give me errors on the calculator which means they do not exist. I do recall that theta should be between [0, pi/2) or [pi, 3pi/2) but there is a final answer in the back of the book (**sqrt(3) - pi/3**)which suggests I am doing something wrong.

Any help would be GREATLY appreciated!

Thanks in advance!