The graph of a function f is shown. Which graph is an antiderivative of f? F

Step 1
Let ${\displaystyle g\left(x\right)}$ be the antiderivative of ${\displaystyle f\left(x\right)}$. Then we must have
${\displaystyle g\left(x\right)=\int f\left(x\right)dx}$
${\displaystyle \Rightarrow g^{\prime }\left(x\right)=f\left(x\right)}$
Now, since ${\displaystyle f\left(x\right)}$ is negative ${\displaystyle (-\mathrm{\infty },p)}$ that means the ${\displaystyle g^{\prime }\left(x\right)}$ is negative in this interval. So, g(x) (the antiderivative of ${\displaystyle f\left(x\right)}$ must be decreasing in this interval. This scenario is shown in two graphs a and b.
Again we notice that ${\displaystyle f\left(x\right)}$ is positive that means, ${\displaystyle g^{\prime }\left(x\right)}$ is positive in ${\displaystyle (p,\mathrm{\infty })}$. So, the function ${\displaystyle g\left(x\right)=}$ antiderivative of ${\displaystyle f\left(x\right)}$ must be increasing in this interval and from the graph we can see that the graph b is increasing after the point ${\displaystyle x=p}$.
So, the correct graph for the antiderivative of ${\displaystyle f\left(x\right)}$ is b.