Use TaskScheduler in directory_lister.cc.

net/base/directory_lister.cc

Index: net/base/directory_lister.cc
diff --git a/net/base/directory_lister.cc b/net/base/directory_lister.cc
index 532ee5db5f8826e6b967e6a8706d39b3ab45aa7d..268648dfd14e766ef32dd8b2433838d8583a88ab 100644
--- a/net/base/directory_lister.cc
+++ b/net/base/directory_lister.cc
@@ -14,6 +14,7 @@
 #include "base/location.h"
 #include "base/logging.h"
 #include "base/task_runner.h"
+#include "base/task_scheduler/post_task.h"
 #include "base/threading/thread_restrictions.h"
 #include "base/threading/thread_task_runner_handle.h"
 #include "base/threading/worker_pool.h"
@@ -79,8 +80,11 @@ DirectoryLister::~DirectoryLister() {
   Cancel();
 }
 
-bool DirectoryLister::Start(base::TaskRunner* dir_task_runner) {
-  return dir_task_runner->PostTask(FROM_HERE, base::Bind(&Core::Start, core_));
+void DirectoryLister::Start() {
+  base::PostTaskWithTraits(
+      FROM_HERE, base::TaskTraits().MayBlock().WithShutdownBehavior(
+                     base::TaskShutdownBehavior::CONTINUE_ON_SHUTDOWN),
+      base::Bind(&Core::Start, core_));
 }
 
 void DirectoryLister::Cancel() {