Double integral in the area verification

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$\iint_D (x^2y+x)dxdy$

Where the area $D$ is limited by curves $y=x^2, y=2x, y=x$

Integrals looks like:

$\int_0^1 dx \int_x^{2x}(x^2y+x)dy + \int_1^2dx \int_{x^2}^{2x}(x^2y+x)dy = ...$

Also second integral:

$\iint_D (2xy+x^2+y)dxdy$

Where the area $D$ is limited by curves $y=x, y=3x, y=-x+4$

$\int_0^1 dx \int_x^{3x}(2xy+x^2+y)dy + \int_1^2dx \int_{x}^{-x+4}(2xy+x^2+y)dy = ...$

Is that correct?