CCA secure vs AE scheme
Let $(\mathsf{Enc},\mathsf{Dec})$ be an authenticated encryption scheme, i.e. it is both IND-CPA secure and INT-CTXT secure (and thus by extension IND-CCA secure). Let $\mathcal{M}$ be the message space of this encrytion scheme and let $\hat m\in\mathcal{M}$ be an arbitrary fixed message.
Now construct the symmetric encryption scheme $(\mathsf{Enc}',\mathsf{Dec}')$ with $\mathsf{Enc}'=\mathsf{Enc}$ and $\mathsf{Dec}'$ defined as
\begin{align*}
&amp;\underline{\mathsf{Dec}'(k,c)}\\
&amp;m := \mathsf{Dec}(k,c)\\
&amp;\textrm{if } m = \bot\\
&amp;\quad \textrm{return } \hat m\\
&amp;\textrm{else}\\
&amp;\quad \textrm{return } m
\end{align*}
It is easy to show that this scheme remains IND-CCA secure. The reduction to the IND-CCA security of $(\mathsf{Enc},\mathsf{Dec})$ merely needs to replace all $\bot$-responses of the decryption oracle with $\hat m$.
At the same time, it is trivial to break INT-CTXT security of $(\mathsf{Enc}',\mathsf{Dec}')$ by simply presenting literally anything as a ciphertext.
This means that if secure authenticated encryption exists, there also exists IND-CCA secure encryption that is not INT-CTXT secure.