Consider the following conformations: 
Statement-I: I$^{nd}$ is more stable than I$^{st}$.
Statement-II: As dihedral angle increases, stability decreases.


| Column-I (Complex compound) | Column-II ($\Delta_0$ (CFSE) $\text{cm}^{-1}$) |
| (i) $[Cr(CN)_6]^{3-}$ | (P) 17000 |
| (ii) $[Cr(H_2O)_6]^{3+}$ | (Q) 15000 |
| (iii) $[Cr(en)_3]^{3+}$ | (R) 12000 |
| (iv) $[CrF_6]^{3-}$ | (S) 20000 |
The value of \[ \int_0^{2} \sqrt{\frac{x(x^2+x+1)}{(x+1)(x^4+x^2+1)}} \, dx \] is