# Reversing the order of integration to solve the double integral

I am trying to solve the double integral:

$$\int_{0}^1\int_{1-x}^{\sqrt(1-x)} e^{{y^2/2}-{y^3/3}} dydx$$

by reversing the order of integration, however, I am unsure how to go about doing it. Is it right to say that initially:

$$\sqrt(1-x) ≤y≤(1-x)$$ and $$0≤x≤1$$. After reversing the order, we get $$1-y^2≤x≤1-y$$ and $$0≤y≤1$$, hence the reversed order of integration will be:

$$\int_{0}^1\int_{1-y}^{1-y^2} e^{{y^2/2}-{y^3/3}} dxdy$$?