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The value of $\int_{-\pi/2}^{\pi/2} \dfrac{dx}{[x] + [\sin x] + 4}$, where $[t]$ denotes the greatest integer less than or equal to $t$, is:
(1) $\dfrac{1}{12}(7\pi + 5)$
(2) $\dfrac{1}{12}(7\pi - 5)$
(3) $\dfrac{3}{20}(4\pi - 3)$
(4) $\dfrac{3}{10}(4\pi - 3)$
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