# Limits of bounded region

While solving a simple problem for finding are of the region bounded by $x=y^2$ and $x=y$. Are the following correct limits?

When $x$ is the outer integration variable $$\int^1_0\int^\sqrt{x}_xdydx$$

When $y$ is the outer integration variable?

$$\int^1_0\int^y_{y^2}dxdy$$

The reason for asking the question is, I am getting the different answer for both the cases which should not be the case.