Find $g(x)$ if the indefinite integral of $f (x)= \begin{cases} -\left(6x+1\right) , & \text{if } x\le 1 \\ -7 , & \text{if } x\ge 1 \end{cases}$ is $$\int f(x) \, dx = \begin{cases} g(x) + C , & \text{if } x\le 1 \\ -7x + C , & \text{if } x\ge 1. \end{cases}$$
$g(x)=$