The integers in the domain of the function $f\left(x\right)={\sin }^{-1}\left(\frac{x^2-3x+2}{x^2+2x+7}\right)$ is/are

$f\left(x\right)={\sin }^{-1}\left(\frac{x^2-3x+2}{x^2+2x+7}\right)$

For domain $$\begin{gathered} \frac{x^2-3x+2}{x^2+2x+7}\ge -1and\frac{x^2-3x+2}{x^2+2x+7}\le 1 \\ \Rightarrow x^2-3x+2\ge -x^2-2x-7,x^2-3x+2\le x^2+2x+7 \end{gathered}$$ and

$\begin{array}{l} \\ 2x^2-x+9\ge 0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{\&}5x\ge -5\ni x\ge -1\\ x\in R,\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}x\in [-1,\mathrm{\infty }]\end{array}$