Evaluate the definite integral $\int_{-1}^{2} \left[ \frac{[x]}{1 + x^2} \right] dx$,where $[\cdot]$ denotes the Greatest Integer Function $(GIF)$.

  • A
    $-2$
  • B
    $-1$
  • C
    $0$
  • D
    None of these

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