Equation for Length of Cubic Spline Between 3 Points

Equation for Length of Cubic Spline Between 3 Points

This is my first time posting here, so I hope this is ok. I'm working on a
java project but my question is really about the math I'll be using for
it...
I have three (different) points at (x1, y1), (x2, y2), and (x3, y3). All I
need is a formula for the length of the cubic spline formed between them.
For someone good at calculus, this should be pretty easy to derive. I've
looked all around online but can't seem to find the solution. Again, I
don't even need the equation of the spline - just its length, given the
three points. Thanks in advance! If someone can figure this out and share,
you'll makey day :)