How do I end a sentence with a quote mid-sentence?
This is a matter of style. Authorities differ on the usage of ellipsis points when a quotation is placed at the end of a sentence, and the quoted material itself is only part of a larger sentence.
The Chicago Manual of Style omits the ellipsis in favour of a sentence-ending period:
John Muir says in his 5th paragraph, "I splashed on through the swamp, strong and exhilarated."
[Note, however, an exception in the case where the sentence as quoted is deliberately incomplete.]
The MLA Handbook places the sentence-ending period after the last word of the quotation, and follows that with an ellipsis:
John Muir says in his 5th paragraph, "I splashed on through the swamp, strong and exhilarated. . . ."
[Regarding a comment made above regarding MLA style for ellipses, it appears that The MLA Handbook dictates that ellipses be enclosed in square brackets only when it is necessary to distinguish these from ellipses in the original quoted text. Refer here, scroll down to Ellipses in Work that Includes Ellipsis.]