A question about automorphism and inner automorphism of $\mathbb{Z}$ $\mathbb{Z}$  is a group under addition. I wish to find $\text{Aut}(\mathbb{Z})$ and $\text{Inn}(\mathbb{Z})$

I know the only automorphism groups of $\mathbb{Z}$ under addition are$\{f(x)=x, f(x)=-x\}$ but what about the inner atomorphisms $\text{Inn} (\mathbb{Z})$?
Refers this question, you can see what $Aut(\mathbb{Z})$ is.

And note that for the ring $R$, the inner automorphisms of R form a normal subgroup of the automorphism group of $R$.
Refers this question, you can see what $Aut(\mathbb{Z})$ is.

And note that for the ring $R$, the inner automorphisms of R form a normal subgroup of the automorphism group of $R$.