The sum of absolute maximum and absolute minimum values of the function \(f(x)=\left|2 x^2+3 x-2\right|+\sin x \cos x\) …

\(3+\frac{\sin \left(1\right){\cos }^{2}\left(\frac{1}{2}\right)}{2}\)

\(3+\frac{1}{2}\left(1+2\cos \left(1\right)\right)\sin \left(1\right)\)

\(5+\frac{1}{2}\left(\sin \left(1\right)+\sin \left(2\right)\right)\)

\(2+\sin \left(\frac{1}{2}\right)\cos \left(\frac{1}{2}\right)\)