Given the functions $f(x)=\{\begin{array}{ccc}-1& if& x<mn>0</mn>\\ x^2+1& if& x0\end{array}$ and $g(x)=\{\begin{array}{ccc}-x^2+1& if& x<mn>0</mn>\\ -1& if& x0\end{array}$

$($a$)$ Find $\underset{xa}{lim}f(x)$ for $a=0^{-},0^{+}$and $0.$

$($b$)$ Find $\underset{xa}{lim}g(x)$ for $a=0^{-},0^{+}$and $0.$

$($c$)$ Find $\underset{xa}{lim}(f(x)+g(x))$ for $a=0^{-},0^{+}$and $0.$