Arc Length Between Two Points of a Curve

(A-Star Math Tournament 2016 Calculus #6) Let $f(x)$ be a function defined for $x\gt 1$ such that $f''(x) = \frac{x}{\sqrt{x^2 -1}}$ and $f'(2) = \sqrt{3}$. Compute the length of the graph of $f(x)$ on the domain $x\in (1, 2]$.