This is just a regular Subversion property. You can extract the value using the following bit of code:
string mergeInfo;
var client = new SvnClient();
bool success = client.GetProperty(
SvnTarget.FromString(fileName),
"svn:mergeinfo",
out mergeInfo);
Note that the GetProperty result does not indicate whether the mergeinfo property was available, but if the method call was successful. The string variable mergeInfo may be null, even if success is correct.
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