Switch to using URLRequestContextBuilder to create some URLRequestContexts.

remoting/remoting_srcs.gypi

 # Copyright 2014 The Chromium Authors. All rights reserved.
 # Use of this source code is governed by a BSD-style license that can be
 # found in the LICENSE file.
 
 {
   'variables': {
     'remoting_base_sources': [
       'base/auth_token_util.cc',
       'base/auth_token_util.h',
       'base/auto_thread.cc',
@@ skipping 17 matching lines @@
       'base/rsa_key_pair.cc',
       'base/rsa_key_pair.h',
       'base/running_average.cc',
       'base/running_average.h',
       'base/scoped_sc_handle_win.h',
       'base/service_urls.cc',
       'base/service_urls.h',
       'base/socket_reader.cc',
       'base/socket_reader.h',
       'base/typed_buffer.h',
-      'base/url_request_context.cc',
-      'base/url_request_context.h',
+      'base/url_request_context_getter.cc',
+      'base/url_request_context_getter.h',
       'base/util.cc',
       'base/util.h',
       'base/vlog_net_log.cc',
       'base/vlog_net_log.h',
       'codec/audio_decoder.cc',
       'codec/audio_decoder.h',
       'codec/audio_decoder_opus.cc',
       'codec/audio_decoder_opus.h',
       'codec/audio_decoder_verbatim.cc',
       'codec/audio_decoder_verbatim.h',
@@ skipping 200 matching lines @@
       'client/plugin/pepper_plugin_thread_delegate.h',
       'client/plugin/pepper_port_allocator.cc',
       'client/plugin/pepper_port_allocator.h',
       'client/plugin/pepper_util.cc',
       'client/plugin/pepper_util.h',
       'client/plugin/pepper_view.cc',
       'client/plugin/pepper_view.h',
     ],
   }
 }