Since we're integrating with respect to y, we have to consider which curve is the 'larger' one horizontally. Sketching both curves yield that is the larger one.
So:
We can see that reversing the order is accounted for by the negative sign.
Okay thank you. I understand the concept, and I figured that was the case but I am having a hard time visualizing that 1/2(x+3) is larger. I have the functions graphed out on my paper, when I rotate the graph 90 degree counterclockwise I can see how 1/2(x+3) is larger...is this how to always look at this type of problem when integrating with respect to y?