Make extensions DSE persistent in browser prefs (Reland)

components/search_engines/template_url_service.h

Index: components/search_engines/template_url_service.h
diff --git a/components/search_engines/template_url_service.h b/components/search_engines/template_url_service.h
index facf0760ceb7ebab34a2b411022a54b9c0974860..ca11382e5e1c88e91ae6292f2555a2d90e1a50cd 100644
--- a/components/search_engines/template_url_service.h
+++ b/components/search_engines/template_url_service.h
@@ -725,13 +725,6 @@ class TemplateURLService : public WebDataServiceConsumer,
   TemplateURL* FindMatchingDefaultExtensionTemplateURL(
       const TemplateURLData& data);
 
-  // Finds the most recently-installed NORMAL_CONTROLLED_BY_EXTENSION engine
-  // that supports replacement and wants to be default, if any. Notifies the
-  // DefaultSearchManager, which might change the effective default search
-  // engine.
-  void UpdateExtensionDefaultSearchEngine();
-
-
   // ---------- Browser state related members ---------------------------------
   PrefService* prefs_;