$\begin{align}  & x\to {{0}^{+}}:x \gt 0\Rightarrow {{x}^{2}} \gt 0\Rightarrow -{{x}^{2}} \lt 0\Rightarrow -2-{{x}^{2}} \lt -2\Rightarrow \underset{x\to {{0}^{+}}}{\mathop{\lim }}\,f\underbrace{(-2-{{x}^{2}})}_{{{(-2)}^{-}}}=-1 \\  & x\to {{(-1)}^{-}}:x \lt -1\Rightarrow {{x}^{2}} \gt 1\Rightarrow -{{x}^{2}} \lt -1\Rightarrow 1-{{x}^{2}} \lt 0\Rightarrow \underset{x\to {{(-1)}^{-}}}{\mathop{\lim }}\,f(\underbrace{1-{{x}^{2}}}_{{{0}^{-}}})=1 \\  & \underset{x\to {{0}^{+}}}{\mathop{\lim }}\,f(-2-{{x}^{2}})-\underset{x\to {{(-1)}^{-}}}{\mathop{\lim }}\,f(1-{{x}^{2}})=-1-1=-2 \\ \end{align}$