Fix issue where side nav wasn't updated every time the route changed.

chrome/test/data/webui/settings/settings_menu_test.js

Index: chrome/test/data/webui/settings/settings_menu_test.js
diff --git a/chrome/test/data/webui/settings/settings_menu_test.js b/chrome/test/data/webui/settings/settings_menu_test.js
index 3f5d5e6f8b220d341500946bc69d414df26ac574..975292759f4e20bb16969d6f8eeaca3919964ad8 100644
--- a/chrome/test/data/webui/settings/settings_menu_test.js
+++ b/chrome/test/data/webui/settings/settings_menu_test.js
@@ -87,6 +87,30 @@ cr.define('settings_menu', function() {
         var path = new window.URL(selector.selected).pathname;
         assertEquals('/reset', path);
       });
+
+      test('navigateToAnotherSection', function() {
+        var selector = settingsMenu.$.subMenu;
+        var path = new window.URL(selector.selected).pathname;
+        assertEquals('/reset', path);
+
+        settings.navigateTo(settings.Route.PEOPLE, '');
+        Polymer.dom.flush();
+
+        path = new window.URL(selector.selected).pathname;
+        assertEquals('/people', path);
+      });
+
+      test('navigateToBasic', function() {
+        var selector = settingsMenu.$.subMenu;
+        var path = new window.URL(selector.selected).pathname;
+        assertEquals('/reset', path);
+
+        settings.navigateTo(settings.Route.BASIC, '');
+        Polymer.dom.flush();
+
+        // BASIC has no sub page selected.
+        assertFalse(!!selector.selected);
+      });
     });
   }