Y=9-x is slope-intercept form of that line, which means it has a slope of -1. Parallel lines have the same slope, so the slope of this new line will also be -1.
To find the line that goes through (5,1), we can use a blank equation y=mx+b. We know that m=-1, so we can use the given point to find b:
No, in general this is not the case. It's only true if for . Otherwise the definite integral gives the *signed* area, which could be negative or even 0.