**Overview**

In AWS it is possible to trigger step functions through an API Gateway integration, see https://docs.aws.amazon.com/step-functions/latest/dg/tutorial-api-gateway.html

Similar integrations already occur within localstack, however the step function URIs are notably missing. See lines 66-88 of https://github.com/localstack/localstack/blob/master/localstack/services/apigateway/apigateway_listener.py



┆Issue is synchronized with this [Jira Bug](https://localstack.atlassian.net/browse/LOC-107) by [Unito](https://www.unito.io/learn-more)

domainName=domain_name
        )
        self.assertEqual(rs['ResponseMetadata']['HTTPStatusCode'], 200)
        self.assertEqual(rs['domainName'], domain_name)
        
        apigw_client.delete_domain_name(domainName=domain_name)
    def _test_api_gateway_lambda_proxy_integration_any_method(self, fn_name, path):
        self.create_lambda_function(fn_name)
        
        lambda_uri = aws_stack.lambda_function_arn(fn_name)
        target_uri = aws_stack.apigateway_invocations_arn(lambda_uri)
        result = testutil.connect_api_gateway_to_http_with_lambda_proxy(
            'test_gateway3', target_uri, methods=['ANY'], path=path, stage_name=self.TEST_STAGE_NAME)
        
        path = path.replace('{test_param1}', 'foo1')
        url = gateway_request_url(api_id=result['id'], stage_name=self.TEST_STAGE_NAME, path=path)
        data = {}
        for method in ('GET', 'POST', 'PUT', 'PATCH', 'DELETE', 'OPTIONS'):
            body = json.dumps(data) if method in ('POST', 'PUT', 'PATCH') else None
            result = getattr(requests, method.lower())(url, data=body)
            if method != 'DELETE':
                self.assertEqual(result.status_code, 200)
                parsed_body = json.loads(to_str(result.content))
                self.assertEqual(parsed_body.get('httpMethod'), method)
            else:
                self.assertEqual(result.status_code, 204)
    def test_apigateway_with_custom_authorization_method(self):
        apigw_client = aws_stack.connect_to_service('apigateway')
        # creat
        lambda_name = 'apigw-lambda-%s' % short_uid()