[integration_test] Add a setter for defaultTestTimeout (#70073)

* [integration_test] Add a setter for defaultTestTimeout

* type annotation

* More type annotations

* Fix doc

packages/integration_test/lib/integration_test.dart

@@ -319,4 +319,13 @@ class IntegrationTestWidgetsFlutterBinding extends LiveTestWidgetsFlutterBinding
     reportData ??= <String, dynamic>{};
     reportData[reportKey] = frameTimes.summary;
   }
+
+  @override
+  Timeout get defaultTestTimeout => _defaultTestTimeout ?? super.defaultTestTimeout;
+
+  /// Configures the default timeout for [testWidgets].
+  ///
+  /// See [TestWidgetsFlutterBinding.defaultTestTimeout] for more details.
+  set defaultTestTimeout(Timeout timeout) => _defaultTestTimeout = timeout;
+  Timeout _defaultTestTimeout;
 }

packages/integration_test/test/binding_test.dart

@@ -87,6 +87,19 @@ Future<void> main() async {
         json.encode(_kTimelines),
       );
     });
+
+    group('defaultTestTimeout', () {
+      final Timeout originalTimeout = integrationBinding.defaultTestTimeout;
+      tearDown(() {
+        integrationBinding.defaultTestTimeout = originalTimeout;
+      });
+
+      test('can be configured', () {
+        const Timeout newTimeout = Timeout(Duration(seconds: 17));
+        integrationBinding.defaultTestTimeout = newTimeout;
+        expect(integrationBinding.defaultTestTimeout, newTimeout);
+      });
+    });
   });
 
   tearDownAll(() async {