**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)

resources = apigw_client.get_resources(restApiId=api_id)
        root_resources = [resource for resource in resources['items'] if resource['path'] == '/']
        root_id = root_resources[0]['id']
        apigw_client.put_method(
            restApiId=api_id, resourceId=root_id, httpMethod='PUT', authorizationType='NONE',
            apiKeyRequired=is_api_key_required
        )
        apigw_client.put_method_response(
            restApiId=api_id, resourceId=root_id, httpMethod='PUT', statusCode='200',
        )
        aws_stack.create_dynamodb_table('MusicCollection', partition_key='id')
        # Ensur
        apigw_client.put_integration(
            restApiId=api_id,
            resourceId=root_id,
            httpMethod='PUT',
            integrationHttpMethod='PUT',
            type='AWS_PROXY',
            uri='arn:aws:apigateway:us-east-1:dynamodb:action/PutItem&Table=MusicCollection',
        )
        apigw_client.put_integration_response(
            restApiId=api_id,
            resourceId=root_id,
            httpMethod='PUT',
            statusCode='200',
            selectionPattern='',
            responseTemplates=response_template)
        apigw_client.create_deployment(restApiId=api_id, stageName='staging')
        return api_id