If \( f(x)=\left|\begin{array}{ccc}x^{2}-4 x+6 & 2 x^{2}+4 x+10 & 3 x^{2}-2 x+16 \\ x-2 & 2 x+2 ...
If \( f(x)=\left|\begin{array}{ccc}x^{2}-4 x+6 & 2 x^{2}+4 x+10 & 3 x^{2}-2 x+16 \\ x-2 & 2 x+2 & 3 x-1 \\ 1 & 2 & 3\end{array}\right| \) and \( \left\{\int_{-2}^{2} x^{2}[f(x)] d x\right\}=2 / k \), when [ ] denotes the greatest integer function, \{\} denotes fractional part; then find the value of \( k \).
(a) 3
(b) 1
(c) 2
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