Questions $3-6$: Let $g(x)={\displaystyle \underset{a}{\overset{x}{}}}f(t)dt$ with the graph of $f$ shown above.

$3.$ State the interval where $g(x)$ is increasing. Justify your reasoning.

$4.$ State the interval where $g(x)$ is concave down. Justify your reasoning.

$5.$ Let $g(1)=4.$ Find the minimum value of $g(x)$ on the interval from $0,4.$ Justify your answer

$g(1)={\displaystyle \underset{0}{\overset{4}{}}}f(t)dt=4$

$6.$ Given $h(x)={\displaystyle \underset{0}{\overset{2x+1}{}}}f(t)dt.$ Find the $x-$value where $h$ has a relative maximum.