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Using the Integrate command against the visible extent, where the cluster tolerance value used is larger than what the rest of the dataset has been integrated to, may create sliver polygons around the edge of the visible extent.
The Integrate command is used to create and manage the adjacency relationships (coincidence) between features within and between layers. This command can be run against the entire dataset or against the visible extent. Running it against the visible extent assumes that the rest of the dataset has been integrated using the same cluster tolerance.
If slivers appear after integration: