Area under y=|x|.

Geometrically, the area is two triangles. If you rotate one of them $90^\circ,$ it makes a unit square: therefore, the area is $\boxed{1}.$

A stricter calculus-based approach can proceed as such: the antiderivatives of $|x|$ are $\frac{1}{2}x^2\times \text{sgn}(x) + C,$ where $\text{sgn}(x)$ is the sign function, and $C$ is an arbitrary constant. The integral is therefore $\int_{-1}^{1} |x| = \frac{1}{2}x^2\text{sgn}(x)\bigg|_{-1}^1 = \boxed{1}$