apigateway: deployment is not invalidated when using a different lambda handler

[eladb]

As described in aws-samples/aws-cdk-intro-workshop#83, when changing a Lambda integration to point to a different handler, the APIGW is not invalidated as it should be.

Reproduction Steps

    // GIVEN
    const stack1 = new Stack();
    const stack2 = new Stack();
    const handler1 = new lambda.Function(stack1, 'handler1', {
      code: lambda.Code.fromAsset(path.join(__dirname, 'integ.cors.handler')),
      runtime: lambda.Runtime.NODEJS_10_X,
      handler: 'index.handler'
    });
    const handler2 = new lambda.Function(stack2, 'handler2', {
      code: lambda.Code.fromAsset(path.join(__dirname, 'integ.cors.handler')),
      runtime: lambda.Runtime.NODEJS_10_X,
      handler: 'index.handler'
    });

    // WHEN
    const api1 = new apigateway.RestApi(stack1, 'myapi', {
      defaultIntegration: new apigateway.LambdaIntegration(handler1)
    });
    const api2 = new apigateway.RestApi(stack2, 'myapi', {
      defaultIntegration: new apigateway.LambdaIntegration(handler2)
    });
    api1.root.addMethod('GET');
    api2.root.addMethod('GET');

    // THEN
    expect(stack1).to(haveResource('AWS::ApiGateway::Stage', {
      DeploymentId: { Ref: 'myapiDeploymentB7EF8EB7e0b8372768854261d2d1218739e0a307' }
    }));
    expect(stack2).to(haveResource('AWS::ApiGateway::Stage', {
      DeploymentId: { Ref: 'myapiDeploymentB7EF8EB77c517352b0f7ab73c333e36585c8f1f3' }
    }));
    test.done();

Error Log

Environment

• CLI Version :
• Framework Version:
• OS :
• Language :

Other

---

This is 🐛 Bug Report