Let $F(x)=\displaystyle \int^{x}_{0} \frac{2-t}{t^{2}+12}\;dt$ for $-\infty<x<+\infty$

(a) Find the value of $x$ where $F$ obtains its maximum value.

$x=$

(b) Find the intervals over which $F$ is only increasing or decreasing. Use interval notation using U for union and enter "none" if no interval.

Intervals where $F$ is increasing:
Intervals where $F$ is decreasing:

(c) Find open intervals over which $F$ is only concave up or concave down. Use interval notation using U for union and enter "none" if no interval.

Intervals where $F$ is concave up:
Intervals where $F$ is concave down: