Close Slivers in Polygon

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I am creating polygons from a text file and am having trouble with the polygons crossing the 180 degree line. The issue is creating rectangular polygons with a sliver cut out of it as seen here:



I am trying to put this into a KML and it is only reading the first portion before the sliver due to it being a multipart polygon (which is probably caused by the sliver).

Now I want to cover the exact area the rectangle covers (therefore, using something like the Minimum Bounding Geometry tool wouldn't be the best). Is there a way to fill in this sliver, essentially tracing the exact boundary of the polygon shapefile?



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