Almost all aviation currencies expire at the end of the calendar month in which they were originally accomplished. There are a very few exceptions to this rule (ie the 90 day landing currency thing).

Your medical would expire on June 1, 2010 (May 31 would be the last day you could legally fly). A possible exception might be if you turn 40 prior to that date (in which case you would have to read the regs to find out for sure.)