Move package:integration_test to flutter/flutter (#69622)

diff --git a/dev/bots/analyze.dart b/dev/bots/analyze.dart
index 3449c3e..9e60c46 100644
--- a/dev/bots/analyze.dart
+++ b/dev/bots/analyze.dart
@@ -270,6 +270,7 @@
   'package:flutter_test/flutter_test.dart',
   'hit_test.dart',
   'package:test_api/src/backend/live_test.dart',
+  'package:integration_test/integration_test.dart',
 };
 
 Future<void> verifyNoTestImports(String workingDirectory) async {
diff --git a/dev/bots/pubspec.yaml b/dev/bots/pubspec.yaml
index 34fc017..bb3a117 100644
--- a/dev/bots/pubspec.yaml
+++ b/dev/bots/pubspec.yaml
@@ -68,7 +68,7 @@
   vm_service_client: 0.2.6+2 # THIS LINE IS AUTOGENERATED - TO UPDATE USE "flutter update-packages --force-upgrade"
   watcher: 0.9.7+15 # THIS LINE IS AUTOGENERATED - TO UPDATE USE "flutter update-packages --force-upgrade"
   web_socket_channel: 1.1.0 # THIS LINE IS AUTOGENERATED - TO UPDATE USE "flutter update-packages --force-upgrade"
-  webkit_inspection_protocol: 0.7.3 # THIS LINE IS AUTOGENERATED - TO UPDATE USE "flutter update-packages --force-upgrade"
+  webkit_inspection_protocol: 0.7.4 # THIS LINE IS AUTOGENERATED - TO UPDATE USE "flutter update-packages --force-upgrade"
   xml: 4.5.1 # THIS LINE IS AUTOGENERATED - TO UPDATE USE "flutter update-packages --force-upgrade"
   yaml: 2.2.1 # THIS LINE IS AUTOGENERATED - TO UPDATE USE "flutter update-packages --force-upgrade"
 
@@ -76,4 +76,4 @@
   mockito: 4.1.1
   test_api: 0.2.19-nullsafety.6
 
-# PUBSPEC CHECKSUM: 07a9
+# PUBSPEC CHECKSUM: 32aa
diff --git a/dev/bots/test.dart b/dev/bots/test.dart
index ac2e00f..304e411 100644
--- a/dev/bots/test.dart
+++ b/dev/bots/test.dart
@@ -678,6 +678,7 @@
     await _runFlutterTest(path.join(flutterRoot, 'examples', 'layers'), tableData: bigqueryApi?.tabledata, options: soundNullSafetyOptions);
     await _runFlutterTest(path.join(flutterRoot, 'dev', 'benchmarks', 'test_apps', 'stocks'), tableData: bigqueryApi?.tabledata);
     await _runFlutterTest(path.join(flutterRoot, 'packages', 'flutter_driver'), tableData: bigqueryApi?.tabledata, tests: <String>[path.join('test', 'src', 'real_tests')]);
+    await _runFlutterTest(path.join(flutterRoot, 'packages', 'integration_test'), tableData: bigqueryApi?.tabledata);
     await _runFlutterTest(path.join(flutterRoot, 'packages', 'flutter_goldens'), tableData: bigqueryApi?.tabledata);
     await _runFlutterTest(path.join(flutterRoot, 'packages', 'flutter_localizations'), tableData: bigqueryApi?.tabledata);
     await _runFlutterTest(path.join(flutterRoot, 'packages', 'flutter_test'), tableData: bigqueryApi?.tabledata, options: soundNullSafetyOptions);