Find the area of the region between the curves y=x^2 - 2x and y = x+4?

Question

so i know that you startout by solving for the intersection points which is
x^2 - 2x = x + 4
x^2 - 2x - x + 4 = 0
(x - 4)(x + 1)=0
x = 4, -1

top= x + 4
bottom=x^2 +2x

then i solve ofr the area
A= ∫ (top - bottom) dx
A=∫ (x + 4 - x^2 +2x)dx
= ∫ (-x^2 + 3x + 4)dx
= -x^3/3 + 3x^2/2 + 4x

then i plug in b into F and a into F and subtract to get the area

the answer i get is 383/8 which is wrong.. so i dont really see what i'm doing wrong.

Answer 1

x^2-2x=x+4
x^2-3x-4=0 x= ((3+-sqrt(25))/2 so x= 4 and x= -1
area = Integral(-1,4) (x+4)-(x^2-2x)dx = Int (-x^2+3x +4)dx=
-x^3/3 +3/2 x^2+4x (-1,4)
= -64/3 +24 +16 +1/3-3/2-4 = -63/3-3/2+36 =-135/6+216/6=
81/6=27/2

Answer 2

i get 193/9 when i plug a and b into F. is that right?