Question

The line y+x=9 intersects the curve y=x^2-2x+3 at the points P and Q .
(a) Find the coordinates of P and Q .
(b) Sketch the line and the curve on the same set of axes.
(c) Calculate the area enclosed by the line and the curve.
Set the two equations equal to each other and solve
Go look at your integration chapter - area bounded by two curve
Integration (line - parabola)dx
Then you are going to deal with adding the part of the parabola under the x-axis

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