Years agao, I had jury duty 1 week before leaving the country for vacation. Where we were living at the time had the system 1 day or 1 trial. If this is your case go the first day and explain there. This way you get credit for showing , not just postponing it.
I explained the situation to the lawyers and would you believe they picked me to serve. The trial was suppose to last only 3 days. We the jury deliberated my last day (leaving in the morning!). Thankfully we came to a decision by lunchtime. The lawyers were getting worried, since I told the turth from the start and there was no alternates, they would have been in trouble with the judge.