The endomorphism is:
Suppose there exists such that , use the Fundamental Theorem of Calculus and you will find a contradiction.
I meant the whole expression "p(x)=0" is not a pol. but an equation, of course.
And in this case it is the zero polynomial, not the zero function. Had he written "p(x):=0" things would
have been clearer (for me, at least).
Ps. By the way, I think my first message shows easily and clearly why the given transf. isn't surjective, but
there hasn't been any discussion on it...