set f(x)=ax^2+bx+c(a is not equal to 0)since f(0)=1, so c=1f(x+1)-f(x)=2x,then a(x+1)^2+b(x+1)-ax^2-bx=2xso 2ax+a+b=2xthat is equal to saya=1,b=-1so f(x)=x^2-x+1