设f(x)=ax^2+bx+c
F(X+1)-F(X)=a(x+1)^2+b(x+1)+c-[ax^2+bx+c]=2ax+a+b=2x
故2a=2,且a+b=解得a=1,b=-1
又f(0)=0,得c=o
综上所述,f(x)=x^2-x