[tex]x + 3 = x^2 + 1\\x + 3 - x^2 - 1 = 0\\x + 2 - x^2 = 0\\\\x^2 - x - 2 = 0\\[/tex]

За т. Вієта:

[tex]\left \{ {{x_{1} +x_{2} =-b} \atop {x_{1} *x_{2} =c}} \right. \left \{ {{x_{1} +x_{2} =1} \atop {x_{1} *x_{2} =-2}} \right. \left \{ {{x_{1}=-1.} \atop {x_{2} =2.}} \right.[/tex]

[tex]S=\int\limits^{2}_{-1} {(x+2-x^2)} \, dx =(\frac{x^2}{2} +2x-\frac{x^3}{3} )|_{-1}^{2} = \frac{2^2}{2} +2*2-\frac{2^3}{3}-(\frac{(-1)^2}{2} +2*(-1)-\frac{(-1)^3}{3})=\frac{9}{2} =\bold{4.5}.[/tex]