\(\left(x-1\right)\left(x-2\right)\left(x-3\right)=0\Rightarrow x=\left\{1;2;3\right\}\)
\(S=\int\limits^3_1\left|\left(x-1\right)\left(x-2\right)\left(x-3\right)\right|dx\)
\(=\int\limits^2_1\left(x-1\right)\left(x-2\right)\left(x-3\right)dx-\int\limits^3_2\left(x-1\right)\left(x-2\right)\left(x-3\right)dx\)
\(=\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{1}{2}\)