设函数 $f\left(x\right)\left(x\in R\right)$满足 $f\left(x+\pi \right)=f\left(x\right)+\sin x$,当 $0\le x<\pi$时, $f\left(x\right)=0$,则 $f\left(\frac{23\pi }{6}\right)=$

$\frac{1}{2}$ $\frac{\sqrt{3}}{2}$ 0 $-\frac{1}{2}$