Firstly, you know you made a mistake when you get a negative area.

You have to know the limits therefore you must calculate the intersections betwen the two curves.

9-x^2=1+2x

From this quatdration equation you can deduce using the Wiet's rule for quadratic formulae that intersections are x= -4 and x=2 which are now the limits.

Then you integrate each of the equations with respect to x from -4 to 2.

When you get the two results for integrals you must (!) take the absolute value for the difference between them. Then you will obtain positive value and true anwser.