Always go back to the general form of the double integral

Now draw the triangle. We clearly see that the top function here is the line . What about a bottem function? Well we can see there are

2 parts here, one from x=0-->x=1 and one from x=1-->x=3

Let us note that we can model sides of a triangle via the line y=mx+b

by doing this we get

for the region

for the region

Now we can integrate our original function from these bounds.

So we get

This should render the desired result