Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be given by $f(x)=(x-1)(x-2)(x-5)$. Define $F(x)=\int_0^x f(t) d t, x>0$. Then which of the following options is/are correct?
Select ALL correct options:
A
F has a local minimum at $\mathrm{x}=1$
B
F has a local maximum at $\mathrm{x}=2$
C
$\mathrm{F}(\mathrm{x}) \neq 0$ for all $\mathrm{x} \in(0,5)$
D
F has two local maxima and one local minimum in $(0, \infty)$
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