\begin{align*} \int_{x \in R} x \frac{1}{12} dx & = \int_{-2}^3 \frac{x}{12} dx + \int_5^6 \frac{x}{12} dx + \int_9^{15} \frac{x}{12} dx\\ & = \frac{9-4}{24} + \frac{36-25}{24} + \frac{225-81}{24}\\ & = \frac{5+11+144}{24} = \frac{160}{24} = \frac{20}{3}. \end{align*}