Let $g(x)=\int_{-3}^{\,x} {f(t)}\,dt,$ where $f$ is the function whose graph is shown below. You can assume the graph of $f$ is symmetric across the $y$-axis.

(a) Evaluate $g(-3)$ and $g(3).$

$g(-3) =$

$g(3) =$

(b) Estimate $g(-2),$ $g(-1),$ and $g(0)$ to the nearest half-unit.

$g(-2) \approx$

$g(-1) \approx$

$g(0) \approx$

(c) Determine the $x$-interval on which $g$ is increasing. If $g$ is never increasing, type "N" in each blank.

$x$-interval: $< x <$

(d) Where does $g$ have its maximum value?

$x =$

Graph of $f$: