Let $k$ be a field and $A=k[X^3,X^5] \subseteq k[X]$.
a. $A$ is a Noetherian domain.
b. $A$ is not integrally closed.
c. $dim(A)=?$ (the Krull dimension).
I suppose that the first follows from $A$ being a subring of $k[X]$, but I don't know about the rest.
Thank you in advance.