Stuck on simple partial integration $$\int_0^3\frac{|x-y|}9dy=\frac19\left(x-\frac32\right)^2+\frac14$$
Could someone enlighten me regarding this partial integration?
I feel like i'm missing something but I dont know what I am doing wrong.

Hint
$$\int_0^3\frac{|x-y|}{9}dy=\int_0^x\frac{x-y}{9}dy+\int_x^3\frac{y-x}{9}dy$$
