Imagine a polar coordinate system with radius = 1. The line that connects these two coordinates is a spiral: (0,0) (10π,1).
How can the length of this spiral be calculated? (Points above are just samples for a "multi rotation" situation... But it can be any two points..)
I'll give a hint on how to setup the problem:
You can use the formula for the arc-length in polar coordinates.
$$ds=\sqrt{r^{2}+(\frac{dr}{dθ})^{2}}dθ$$
with $L=\int ds$.
With a standard spiral you have r to be a linear function of theta $r(\theta) = r_{0}+b(\theta - \theta_{0})$.