\left| \displaystyle \int_{-3}^{2}x^2+x-6 dx \right|= \left| \left \frac{x^3}{3} + \frac{x^2}{2} - 6x \right|_{-3}^2 \right|= \left| \frac{8}{3} + 2 -12 + 9 - \frac{9}{2} - 18\right| = \frac{89}{6}