Alright so the problem:

Find the reigon in the xy plane that is bounded by the curves:

x = y^2

and

2y + x = 3

quickly solving for the y coordinates of intersection, i get

y = -3 and 1

so using horizontal components i got:

3-2y - y^2

and then integrating and quickly solving i get 32/3 as a final answer

do the steps seem alright or have i made a mistake somewhere?

Many thanks