Hi,

I'm learning about reparametrizing curves and I don't understand what my teacher did in the following example :

Reparametrize the helix $\displaystyle (\cos t, \sin t, t)$ from $\displaystyle (1,0,0)$ in the same direction than $\displaystyle t$ increases.

Solution: $\displaystyle s(t)=\int_0^t |r'(u)| du$.

Then she continues from this and I understand all she did.

What I don't understand is why the lower bound of the integral is 0.

It's sometimes different from 0, so how do I know what lower bound to chose? I'm sure it's because of the (1,0,0) point, but why 0 as lower bound? Is it because the z-coordinate is worth 0 in (1,0,0)?