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

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);