Let \( f(x) \) be a function defined by \( f(x)=\int_{1}^{x} t\left...

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Let \( f(x) \) be a function defined by \( f(x)=\int_{1}^{x} t\left(t^{2}-3 t+2\right) d t, 1 \leq x \leq 3 \). Then, the range of \( f(x) \) is
\( \mathrm{P} \)
(a) \( [0,2] \)
(b) \( \left[-\frac{1}{4}, 4\right] \)
(c) \( \left[-\frac{1}{4}, 2\right] \)
(d) None of these
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