how do I integrate a modulus function. is it possible? I am solving a question in which after calculating, my instantaneous velocity is  $f(t)=\frac{ab\sin(bt)}{\sqrt{2-2\cos(bt)}}$.
So I need to find distance in time $T$. For finding distance I need to take its modulus and integrate
$|f(t)|$dt. 
So how do I find integral of
$|f(t)|$dt.
Any hints are appreciable.
Thanks in advance.

\begin{align*}
  \left| \frac{ab\sin bt}{\sqrt{2-2\cos bt}} \right| &=
  \left|
    \frac{2ab\sin \frac{bt}{2} \cos \frac{bt}{2}}{\sqrt{4\sin^{2} \frac{bt}{2}}}
  \right| \\
  &= \left| ab\cos \frac{bt}{2} \right| \\
 s &= \int_{0}^{t} \left| ab\cos \frac{bt}{2} \right| dt \\
   &= 2a E \left( \frac{bt}{2}, 1 \right)
\end{align*}

where $\displaystyle E(\theta,k)=\int_{0}^{\theta} \sqrt{1-k^{2} \sin^{2} \phi} \, d\phi$ is the elliptic integral of the second kind.
In this case, $$E \left( \frac{bt}{2},1 \right)=
2\left \lfloor \frac{bt}{2\pi}+\frac{1}{2} \right \rfloor+
(-1)^{\left \lfloor \frac{bt}{2\pi}+\frac{1}{2} \right \rfloor} \sin \frac{bt}{2}$$

