I am reading on derived categories and am given the definition $\operatorname{Ext} _\mathcal{A}^k\left( {M,N} \right) = {\operatorname{Hom} _{\operatorname{D} \left( \mathcal{A} \right)}}\left( {M,N\left[ k \right]} \right)$.
However I am more familiar with the definition $\operatorname{Ext} _\mathcal{A}^k\left( {M,N} \right) = \left( {{R^k}{{\operatorname{Hom} }_\mathcal{A}}\left( {M, - } \right)} \right)\left( N \right)$.
How can I show that these are the same?