The answer is
I've tried plugging in 2 for x and 1 for x, but I'm not coming up with the answer.
Whoa. That is markedly different than what you had. What you had simply said "evaluate the integral from 1 to 2". Which is what we're doing when finding arc-length.
So we have an equation of the form
is equal to the arc-legth of from to .
So from your equation we need to find the derivative of:
Which is equal to:
Plugging this into our equation for arc length yields:
Can you distribute that squared and go from there?