Integral of Sinx with absolute value

Question

Which one is correct?

in Microsoft Mathematics :

in Wolfram Alpha :

and what does $\mathrm{sgn} (\sin x)$ mean ?

Finally, what is the answer to this integral?

Answer 1

Both are correct.

In the first case, the integrand was $\sin X$ (note the uppercase) which is independent of $x$. In the second case, the integrand was $\sin x$ which is a function of $x$.

$\operatorname{sgn}(x)$ is the sign function: $$ \operatorname{sgn}(x) = \begin{cases} \begin{align} 1 &: x > 0, \\ 0 &: x = 0,\\ -1 &: x < 0. \end{align} \end{cases} $$