The derivation of the formula is here:
Arc length - Wikipedia, the free encyclopedia
If f is a continuously differentiable function, show how to establish the formula
L = (integral from a to b) (root)(1 + (f'(x))^2) dx
for the length of the curve y = f(x) between (a, f(a)) and (b, f(b)).
I don't know how to proceed, but I do know that the regular formula for arclength is L(x) = (integral from a to b) ||x'(t)||dt. Any help? Thanks!