Add support for log file rotation.

ui/file_manager/file_manager/background/js/media_import_handler.js

Index: ui/file_manager/file_manager/background/js/media_import_handler.js
diff --git a/ui/file_manager/file_manager/background/js/media_import_handler.js b/ui/file_manager/file_manager/background/js/media_import_handler.js
index 9065e05b120e19d08378e89f0339d2ef3238d912..94974a08426287a676986aff6c8b778407039886 100644
--- a/ui/file_manager/file_manager/background/js/media_import_handler.js
+++ b/ui/file_manager/file_manager/background/js/media_import_handler.js
@@ -256,7 +256,7 @@ importer.MediaImportHandler.ImportTask.prototype.run = function() {
   this.scanResult_.whenFinal()
       .then(this.initialize_.bind(this))
       .then(this.importScanEntries_.bind(this))
-      .catch(importer.getLogger().catcher('import-task-chain'));
+      .catch(importer.getLogger().catcher('import-task-run'));
 };
 
 /**
@@ -337,7 +337,8 @@ importer.MediaImportHandler.ImportTask.prototype.importOne_ =
               return this.copy_(entry, destinationDirectory);
             }
           }.bind(this))
-      .then(completionCallback);
+      .then(completionCallback)
+      .catch(importer.getLogger().catcher('import-task-import-one'));
 };
 
 /**
@@ -422,7 +423,8 @@ importer.MediaImportHandler.ImportTask.prototype.copy_ =
                 onComplete.bind(this),
                 onError.bind(this));
           }.bind(this),
-          resolver.reject);
+          resolver.reject)
+      .catch(importer.getLogger().catcher('import-task-copy'));
 
   return resolver.promise;
 };
@@ -455,7 +457,8 @@ importer.MediaImportHandler.ImportTask.prototype.markAsCopied_ =
             entry,
             this.destination_,
             destinationUrl);
-      }.bind(this));
+      }.bind(this))
+      .catch(importer.getLogger().catcher('import-task-mark-as-copied'));
 };
 
 /**
@@ -469,7 +472,8 @@ importer.MediaImportHandler.ImportTask.prototype.markAsImported_ =
       /** @param {!importer.ImportHistory} history */
       function(history) {
         history.markImported(entry, this.destination_);
-      }.bind(this));
+      }.bind(this))
+      .catch(importer.getLogger().catcher('import-task-mark-as-imported'));
 };
 
 /** @private */