\begin{align*} \int_{x \in R} x^2 \frac{1}{12} dx - \mu^2 & = \int_{-2}^3 \frac{x^2}{12} dx + \int_5^6 \frac{x^2}{12} dx + \int_9^{15} \frac{x^2}{12} dx - \mu^2\\ & = \frac{81+8}{36} + \frac{216-125}{36} + \frac{3375-729}{36} - \big ( \frac{20}{3} \big )^2\\ & = \frac{89+91+2646}{36} - \frac{400}{9} = \frac{2826-1600}{36} \\ & = \frac{1226}{36} \approx 34.055. \end{align*}