$($Review from last week$)$ Consider the function $F(x)={\displaystyle \underset{0}{\overset{x}{}}}2tdt.$

$($a$)$ The function $F$ inputs a real number $x.$ Which of the following describes the output of the function $F$ in words?

I. The output of $F$ is the area under the graph of $y=2t$ between $0$ and the input $x$

II$.$ The output of $F$ is the slope of the tangent line to the graph $y=2t$ at the input $x.$

III. The output of $F$ is simply $2$ times the input $x.$

IV$.$ The output of $F$ is the maximum value of $2t$ between $0$ and the input $x$