Let $R$ be commutative Noetherian ring but not necessary local ring, and $I$ be proper ideal of $R$. I want to find an example of ring such that

$Ext_R^i(R/I,R)\neq 0$ is not zero at least in two point and finite time. on the other hand $grade(R/I,R)\neq injdim(R)$, and $injdim(R)$ is finite.

Let $R$ be commutative Noetherian ring but not necessary local ring, and $I$ be proper ideal of $R$. I want to find an example of ring such that

$\operatorname{Ext}_R^i(R/I,R)\neq 0$ is not zero at least in two point and finite time. on the other hand $\operatorname{grade}(R/I,R)\neq \operatorname{injdim}(R)$, and $\operatorname{injdim}(R)$ is finite.