Let $g(x)=\int_{0}^{\,x} {f(t)}\,dt,$ where $f$ is the function whose graph is shown below.

(a) Evaluate $g(0),$ $g(1),$ $g(2),$ $g(3),$ and $g(6).$

$g(0) =$

$g(1) =$

$g(2) =$

$g(3) =$

$g(6) =$

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

$x$-interval: $< x <$

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

$x =$

Graph of $f$: