Example $11\mathrm{.}1$: Given

$|)(y|)|)(x|)f_{xY}(x,y)dxdy={\displaystyle \underset{0}{\overset{1}{}}}{\displaystyle \underset{0}{\overset{y}{}}}kdxdy={\displaystyle \underset{0}{\overset{1}{}}}kydy=\frac{k}{2}=1=>k=2.f_Y(y)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{f}_{xY}(x,y)dx={\displaystyle \underset{0}{\overset{y}{}}}kdx=ky,0f_x(x)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{f}_{xY}(x,y)dy={\displaystyle \underset{x}{\overset{1}{}}}kdy=k(1-x),0$

and

$f_Y(y)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{f}_{xY}(x,y)dx={\displaystyle \underset{0}{\overset{y}{}}}kdx=ky,0$

How did we decided the limits of integration pointed out by blue marker?