Fix shutdown race when running Dart on the message loop

services/dart/content_handler_main.cc

Index: services/dart/content_handler_main.cc
diff --git a/services/dart/content_handler_main.cc b/services/dart/content_handler_main.cc
index ad599cc096e18051018c21c42cd8d43a04481466..219f2be310a88b39233aa58d7c9fe7d2cd42ca44 100644
--- a/services/dart/content_handler_main.cc
+++ b/services/dart/content_handler_main.cc
@@ -140,7 +140,11 @@ class DartContentHandlerApp : public mojo::ApplicationDelegate {
         default_strict_(false),
         run_on_message_loop_(false) {}
 
-  ~DartContentHandlerApp() override {}
+  ~DartContentHandlerApp() override {
+    // Shutdown the controller.
+    mojo::dart::DartController::Shutdown();
+    delete service_connector_;
+  }
 
   void ExtractApplication(base::FilePath* application_dir,
                           mojo::URLResponsePtr response,
@@ -242,13 +246,6 @@ class DartContentHandlerApp : public mojo::ApplicationDelegate {
     return true;
   }
 
-  // Overridden from ApplicationDelegate:
-  void Quit() override {
-    // Shutdown the controller.
-    mojo::dart::DartController::Shutdown();
-    delete service_connector_;
-  }
-
   mojo::TracingImpl tracing_;
   DartContentHandler content_handler_;
   DartContentHandler strict_content_handler_;