I am reading Sharp: Steps in Commutative Algebra, Chapter 2: Ideals. (see attached pages 18-19 for Sharp's definitions etc)

On page 19 Sharpe gives the following exercise

2.4 EXERCISE

Let X be an indeterminate and consider the ring [X] of polynomials in X with co-efficients in

Give

(i) an example of a subring of [X] which is not an ideal of [X]

and

(ii) an example of an ideal of [X] which is not a subring of [X]

I would appreciate help with this exercise.

Peter