Equivalences between categories $\mathcal{K}^b(\text{Injectives})$ and $\mathcal{D}^b(\mathcal A)$ if $\mathcal{A}$ has enough injectives

Question

I have the following question:

Let $\mathcal{A}$ be a abelian category and $\mathcal{I}$ be the full subcategory of injective objexts of $\mathcal{A}$. Assume that $\mathcal{A}$ has enough injectives. Let $\mathcal{K}^b(\mathcal{I})$ be the homotopy category of (bounded)-complexes of $\mathcal{I}$, and $\mathcal{D}^b(\mathcal A)$ be the bounded derived category of $\mathcal{A}$. Is it true that $\mathcal{K}^b(\mathcal{I})$ and $\mathcal{D}^b(\mathcal A)$ are equivalent? Thanks very much!