[tex]S=\int\limits^4_0 {(x^2-4x+5)} \, dx = \frac{4^3}{3}-2*4^2+5*4-(\frac{0^3}{3}-2*0^2+5*0 )=\frac{28}{3}. \\\int\limits {(x^2-4x+5)} \, dx = \frac{x^3}{3}-2x^2+5x.[/tex]

Ответ:

[tex]\frac{28}{3}.[/tex]