Given below are two statements:
Statement I: Benzene is nitrated to give nitrobenzene, which on further treatment with \( \text{CH}_3\text{COCl} / \text{AlCl}_3 \) will give the product shown. 
Statement II: \( -\text{NO}_2 \) group is a meta-directing and deactivating group.
In the light of the above statements, choose the most appropriate answer from the options given below.


The value of \[ \int_0^{2} \sqrt{\frac{x(x^2+x+1)}{(x+1)(x^4+x^2+1)}} \, dx \] is