The diagram shows a sketch of part of the curve with equationy=x2+1 and the line with equationy=7−x. The finite regionR1 is bounded by the line and the curve. The finite regionR2 is below the curve and the line and is bounded by the positivex- andy-axes as shown in the diagram.

(a) Find the area ofR1.

(b) Find the area ofR2.

$\displaystyle 7-x = x^2 + 1 $

$\displaystyle 0 = x^2 + x -6 $

$\displaystyle 0 = (x+3) (x-2) $

$\displaystyle x = 2 , x = -3 $

Area of R1 = $\displaystyle \int_{-3}^2 [ 7-x-x^2 + 1] dx $

I can work this out, but How would I go about working the area of region 2? Becasue there's also the area of region 1 inside region 2.