update_engine: fixed remaining linter and some spelling errors

Fixed remaining errors from cpplint as well as some spelling errors
mostly in comments.

BUG=None
TEST=FEATURES=test emerge-link update_engine

Change-Id: I484988ab846ac5a3c68c016ddccfb247f225ec27
Reviewed-on: https://chromium-review.googlesource.com/208897
Reviewed-by: Alex Vakulenko <avakulenko@chromium.org>
Commit-Queue: Alex Vakulenko <avakulenko@chromium.org>
Tested-by: Alex Vakulenko <avakulenko@chromium.org>
diff --git a/update_manager/real_time_provider.cc b/update_manager/real_time_provider.cc
index 9067bdd..e9ac3c2 100644
--- a/update_manager/real_time_provider.cc
+++ b/update_manager/real_time_provider.cc
@@ -4,6 +4,8 @@
 
 #include "update_engine/update_manager/real_time_provider.h"
 
+#include <string>
+
 #include <base/time/time.h>
 
 #include "update_engine/clock_interface.h"