x^2-2x+1=-x^2+3x-1
2x^2-5x+2=0
D=25-16=9
x_(1)=(5-3)/4=0,5 ; x_(2)=(5+3)/4=2
S= ∫ ^(2)_(0,5)((-x^2+3x-1)-(x^2-2x+1))dx=
= ∫ ^(2)_(0,5)(-2x^2+5x-2)dx=
=(-2x^3/3)+(5x^2/2)-2x)|^(2)_(0,5)=
=(-2/3)*(2^3-0,5^3)+(5/2)(2^2-0,5^2)-2*(2-0,5)=
=(-2/3)*(63/8) +(5/2)*(15/4)-3=(-42/8)+(75/8)-3=(33-24)/8=9/8