Below is the graph of $f(t).$

$($a$)$ If $F(x)={\displaystyle \underset{0}{\overset{x}{}}}f(t)dt,$ which of the graphs given below could be a graph of $F(x)?$

Explain your criterion.

$($b$)$ If $G(x)={\displaystyle \underset{-2}{\overset{x}{}}}f(t)dt,$ which of the graphs given below could be a graph of $G(x)?$