Let \( f(a, b)=\int_{a}^{b}\left(x^{2}-4 x+3\right) d x,(ba) \) the...

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Let \( f(a, b)=\int_{a}^{b}\left(x^{2}-4 x+3\right) d x,(ba) \) then
(A) \( f(a, 3) \) is least when \( a=1 \)
(B) \( f(4, b) \) is an increasing function \( \forall b \geq 4 \)
(C) \( f(0, b) \) is least for \( b=2 \)
(D) \( \min \{f(a, b)\}=-\frac{4}{3} \)
\( \mathrm{P} \)
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