Chapter 5 - The Integral - 5.4 The Fundamental Theorem of Calculus, Part I - Exercises - Page 258: 35

$$\frac{97}{4}.$$

We have $$ \int_{-2}^{3}|x^3| d x= \int_{-2}^{0}|x^3 |d x+\int_{0}^{3}|x^3|d x\\ = -\int_{-2}^{0}x^3 d x+\int_{0}^{3}x^3d x=-\frac{1}{4}x^4|_{-2}^{0}+\frac{1}{4}x^4|_{0}^{3}\\ =4+\frac{81}{4}=\frac{97}{4}. $$