Let  $f:ℝ\to ℝ$ be given by $f\left(x\right)=\left(x-1\right)\left(x-2\right)\left(x-5\right)$ 

 Define $F\left(x\right)=\underset{0}{\overset{x}{\int }}f\left(t\right)dt,x>0$   

Then when of the following options is/are correct?

$F^1\left(x\right)=f\left(x\right)=(x-1)(x-2)(x-5)$

$\text{ At }x=1\text{ and }x=5 F\left(x\right)\text{ has local minima }$

$\text{ At }x=2,F\left(x\right)\text{ has local maxima and }F\left(x\right)<0\forall x\in (0,5)$       $\left(\sin ce F \left(x\right) has local maximum at x=2 and maximum mavalue F\left(2\right)={\int }_0^2\left(x-1\right)\left(x-2\right)\left(x-5\right)dx<0\right)$

  $f\left(x \right) graph is$

   The graph of F(x) is