Chapter 5 - The Integral - 5.4 The Fundamental Theorem of Calculus, Part I - Exercises - Page 258: 33

$\frac{5}{2}.$

We have $$ \int_{-2}^{1}|x| d x= \int_{-2}^{0}|x| d x+ \int_{0}^{1}|x| d x\\ = -\int_{-2}^{0}xd x+ \int_{0}^{1}x d x =-\frac{1}{2}x^2|_{-2}^0+\frac{1}{2}x^2|_{0}^1\\ =-\frac{1}{2}(0-4)+\frac{1}{2}=\frac{5}{2}. $$