Pick 2 numbers : one from interval [0,1] and second one from interval [0,2]. Calculate the probability that the absolute value of the difference between the numbers is greater than one.

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I defined 2 numbers : $x \in [0,1]$ $y\in[0,2]$. I've been thinking on this problem and came up with a few ideas, but sketching a graph and calculating the field is the easiest (I think). I used the definition of an absolute value and got $x-y>1 \equiv y<x-1 $ - doesn't work since $y\in[0,2]$. $x-y<-1 \equiv y>x+1$. I drew a simple sketch and calculated the area : $1\cdot1\cdot\cfrac{1}{2} = \cfrac{1}{2}$. Is it correct? If it is, how to solve this task without drawing anything, this is using integrals?