I'm not getting that 4. I'm getting only $\dfrac {2x}{\pi}$
Consider the integral
\begin{equation}
I(x)= \frac{1}{\pi} \int^{\pi}_{0} sin(xsint) dt
\end{equation}
show that
\begin{equation}
I(x)= 4+ \frac{2x}{\pi}x +O(x^{3})
\end{equation}
as $x\rightarrow0$.
=> I Have used the expansion of McLaurin series of $I(x)$ but did not work.
please help me.