Length of Curve (Parametric)

Find the length of the following parametric curve

$\displaystyle y= a(cos t + ln tan \frac {t}2$)

$\displaystyle y= a sint$

from the point (0,a) to the point (x,y).

I need to use the formula

$\displaystyle L= \int \sqrt{( \frac {dx}{dt}^2)+ (\frac {dy}{dt}^2)}dt$

but I'm not sure what the limits of integration are so I can evaluate the result.

As well, would $\displaystyle \frac {dx}{dt}$ be $\displaystyle a(-sin t+ \frac {1}{tan \frac {t}2})$? Or am I differentiating the ln incorrectly?