The sum of absolute maximum and absolute minimum values of the function \( f(x)=\left|2 x^{2}+3 ...

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The sum of absolute maximum and absolute minimum values of the function \( f(x)=\left|2 x^{2}+3 x-2\right|+\sin x \cos x \) in the interval \( [0,1] \) is
(a)
\( 3+\frac{\sin (1) \cos ^{2}\left(\frac{1}{2}\right)}{2} \)
(b) \( 3+\frac{1}{2}(1+2 \cos (1)) \sin (1) \)
(c) \( 5+\frac{1}{2}(\sin (1)+\sin (2)) \)
(d) \( 2+\sin \left(\frac{1}{2}\right) \cos \left(\frac{1}{2}\right) \)
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