f(x)=ax方+bx+c (1)
则f(0) = c,又f(0)=0,所以 c=0
f（x+1）=f（x）+x+1
当x=0时,有f(1) = f(0) + 0 + 1 = 1;
当x =-1时,有f(0) = f(-1)-1+1=0 即 f(-1)=0
将(1)式中代入x=1,x=-1有
f(1) = a+b =1 (2)
f(-1) = a -b =-1 (3)
(2)+(3) ,有2a = 0,a=0
(2)-(3),有2b = 2,b=1
所以a = 0,b=1,c=0
所以f(x) = x