I think the region you're supposed to evaluate starts at y=1, has a right edge where the green and red graphs intersect, and an upper bound where the green graph crosses the y-axis again, which should be at y=7.
So because of the way the region is set up, we should integrate with respect to y instead of x. That means we need to solve both equations for x.
So looking at the region it looks like it's good to break it up into two smaller regions. From y=1 to where the graphs intersect, the x-values of the region are defined by
and after they intersect until y=7 the x-values are defined by
So let's figure out where they intersect.
So I think the whole are is:
Does that make sense? Hopefully I don't have any huge errors.