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3 added 157 characters in body; edited tags

I am desperately looking for an integral domain $A$ with the following properties:

1. $A$ is not integrally closed
2. $A$ has a quotient field $K$ that is algebraically closed and that has characteristic 0
3. There is an integral element $x\in K$ (over $A$) such that $A[x]$ is integrally closed.

Can someone help to tell me if the above is even possible?

Edit: Lubin easily gave me an example. Now I want to consider the case when I replace the condition 2. by:

2'. $A$ has a quotient field $K$ that is real closed.

2 added 6 characters in body

I am desperately looking for an integral domain $A$ with the following properties:

1. $A$ is not integrally closed
2. $A$ has a quotient field $K$ that is algebraically closed and that has characteristic 0
3. There is an integral element $x\in K$ of (over $A$ A$) such that$A[x]$is integrally closed. Can someone help to tell me if the above is even possible? 1 normal domains with algebraically closed quotient field I am desperately looking for an integral domain$A$with the following properties: 1.$A$is not integrally closed 2.$A$has a quotient field$K$that is algebraically closed and that has characteristic 0 3. There is an integral element$x\in K$of$A$such that$A[x]\$ is integrally closed.

Can someone help to tell me if the above is even possible?