The value of the integral ∫limits_-1^1|x| dx is :

$I = \int\limits_{-1}^1|x| dx$

|x| is even function

$\int\limits_{-a}^a f(x) dx = 2\int\limits_{0}^a f(x) dx$ if f(x) is even

$I = 2 \int\limits_{0}^1|x| dx$

$= 2 \int\limits_{0}^1|x| dx$ as |x| = x  in (0, 1)

$=2\left[\frac{x^2}{2}\right]_0^1$

= 1 sq. units