#### Answer

The function has an absolute maximum equal to $5$ and an absolute minimum equal to $-4$ over the specified interval.

#### Work Step by Step

$h'(x)=-2x.$
$h'(x)$ is defined for all x in the interval.
$h'(x)=0\to x=0;$ hence, $x=0$ is, along with the endpoints of the interval, a possible candidate for an absolute extrema.
$h(-3)=-4.$
$h(0)=5.$
$h(1)=4.$
The function has an absolute maximum equal to $5$ and an absolute minimum equal to $-4$ over the specified interval.