Let $F(x)={\displaystyle \underset{2}{\overset{x}{}}}f(t)dt.$ The graph of $f$ on the interval $-2,6$ consists of two$-$line segments and a quarter of a circle, as shown below.

a$.$ Fill out the table below.

$\backslash$table$[[x,-2,-1,0,1,2,4,5,6],[F(x),,,,,,,,]]$

b$.$ Determine the interval where $F(x)$ is increasing. Justify your answer.

c$.$ Find the critical numbers of $F(x)$ and determine if each corresponds to a relative minimum value, a relative maximum value, or neither. Justify your answers.

d$.$ Find the absolute extreme values of $F(x)$ and the $x-$values at which they occur. Justify your answers.

e$.$ Find the $x-$coordinates of the inflection points of $F(x).$ Justify your answer.

f$.$ Determine the intervals where the graph of $F(x)$ is concave down. Justify your answer.

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