Answer
Neither.
Work Step by Step
a. Evaluating the integral, we have $\int_{-1}^1(2x)dx=x^2|_{-1}^1=1^2-(-1)^2=0$
which is not the area of the shaded region.
b. Evaluating the integral, we have $\int_{-1}^1(-2x)dx=-x^2|_{-1}^1=-1^2+(-1)^2=0$
which is not the area of the shaded region.
We can conclude that neither expression gives the correct answer. To calculate the shaded area, we have
$A=\int_{-1}^0(-x-x)dx+\int_0^1(x-(-x))dx=-x^2|_{-1}^0+x^2|_0^1=(-1)^2+(1)^2=2$
