The function $f$ is defined piecewise as follows.

$f(x)=\{\begin{array}{ccc}{x}^2+3x-1& if& x<mn>1</mn>\\ x+2& if& x>1\end{array}$

Find the following limits$.$

If a limit does not exist, click on "Does Not Exist."

$($a$)\underset{x{1}^{-}}{lim}f(x)=$

$($b$)\underset{x{1}^{+}}{lim}f(x)=$

$($c$)\underset{x1}{lim}f(x)=$