Let $$f(x) = \begin{cases} 0 & \text{if } x < -5 \\ 5 & \text{if } -5 \leq x < -1 \\ -3 & \text{if } -1 \leq x < 5 \\ 0 & \text{if } x \geq 5 \end{cases}$$ and $$g(x) = \int_{-5}^{x}\, f(t) dt$$
Determine the value of each of the following:
(a) $g(-7) =$
(b) $g(-4) =$
(c) $g(0) =$
(d) $g(6) =$
(e) The absolute maximum of $g(x)$ occurs when $x =$ and is the value

It may be helpful to make a graph of $f(x)$ when answering these questions.