Double integration to find the area of a bounded region

**The question**

Use double integration to find the area bounded by $\displaystyle y = x^3$ and $\displaystyle y = x^2$

**My attempt**

I know that finding the area of a bounded region is given by:

$\displaystyle \iint_\Omega {1 \ dx\ dy}$

So I drew the graph and decided to attempt it by taking two integrals:

$\displaystyle \int_0^x\int_{x^2}^{x^3} {1 \ dy\ dx}$ +

$\displaystyle \int_{-x}^0\int_{x^3}^{x^2} {1 \ dy\ dx}$

But upon solving these I get $\displaystyle \frac{-2x^3}{3}$ rather than the solution $\displaystyle \frac{1}{12}$

I'm fairly sure I'm attempting this wrong. :/

Any help would be most appreciated!