Do not use technology.

Let

F$($x$)=\backslash$int$\_3^$x f$($t$)$dt

The graph of f on the interval $-3,4$ consists of two line segments and a semicircle, as shown in the graph.

$($a$)$ Find F$(0),$F$^(\text{'})(0),$ and F$(4).$

Write the equation of the line tangent to F$($x$)$ at the point where

x $=2.$

y$($x$)=$