$(1)(10$ pts$)$ Consider the accumulation function $F(x)={\displaystyle \underset{-1}{\overset{a}{}}}g(t)dt$ on the interval $-4,5.$ The graph of the integrand $y=g(t)$ is given below on the interval $-4,5.$

$($a$)$ Which of the following describes $F(0)?$

$F(0)>0.$

$F(0)=0.$

Not enough evidesce to justily any of the descriptions.

$($b$)$ Evaluate $F(3).$

$F(3)=2$

$($c$)$ Determine the interval$($s$)$ where $F$ is increasing on the interval $-4,5.$

$($d$)$ Approximate the $x-$value at which $\frac{dF}{dx}$ activeves its absolute minimum on the interval $(-4,5].$

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$($c$)$ Determine the $x-$value at which $F$ achieves its absolute minimum on the interval $-4,5.$