Hi, given a polynomial, how can one find another from it satisfying a condition. E.g if a given polynomial equation is f(x) ,we need to find another polynomial , g(x) ,with the relation that g(0)=0 and g(x)-g(x-1)=f(x).

E.g if f(x)=2x-1 then the required g(x)=x^2 .

Do we need to use integration here?

Thanks.