integral of $\arcsin(\sin(x))$ I'm having trouble with this integral
$$\int\arcsin(\sin x)\,\mathrm dx$$
The problem is with the intervals of definition for each function :/ if someone could dumb it down for me.   


*

*$\arcsin\colon [-1, 1] \to [-\pi/2, \pi/2]$.  

*$\sin:\mathbb{R}\to [-1, 1]$.


right?
But what about $\arcsin(\sin x)$ ?

Since $\sin(x)$ can take $ \mathbb R$ and outputs $[-1, 1]$ and $\arcsin(x)$ can take $[-1, 1]$ and output $[-\pi/2, \pi/2]$ , then it stands to reason that the constraints for $\arcsin(\sin(x))$ would be $\mathbb R \rightarrow [-\pi/2, \pi/2]$.
