Answer: the correct use of comma in the statement is "The Carl G. Jung exhibition runs from June 17, to September 25, 2010".
Explanation: commas are one of the punctuations mark, that is used to separate words and phrases in a sentence, so that the reader can have a little time to rest before completing the sentence.
One of the syntax in English language is that comma should be used immediately after the day and month in a sentence. It makes the sentence to be less stressful for the readers to read.
In this statement comma sign has been used immediately after the day and month, in obedience to the syntax of the language.