**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)

return invoke_rest_api(api_id, stage, method, relative_path_w_query_params,
            data, headers, path=path, context=context)
    except AuthorizationError as e:
        return make_error_response('Not authorized to invoke REST API %s: %s' % (api_id, e), 403)
def invoke_rest_api(api_id, stage, method, invocation_path, data, headers, path=None, context={}):
    path = path or invocation_path
    relative_path, query_string_params = extract_query_string_params(path=invocation_path)
    
    authorize_invocation(api_id, headers)
    path_map = helpers.get_rest_api_paths(rest_api_id=api_id)
    try:
        extracted_path, resource = get_resource_for_path(path=relative_path, path_map=path_map)
    except Exception:
        return make_error_response('Unable to find path %s' % path, 404)
    api_key_required = resource.get('resourceMethods', {}).get(method, {}).get('apiKeyRequired')
    if not is_api_key_valid(api_key_required, headers, stage):
        return make_error_response('Access denied - invalid API key', 403)
    integrations = resource.get('resourceMethods', {})
    integration = integrations.get(method, {})
    if not integration:
        integration = integrations.get('ANY', {})
    integration = integration.get('methodIntegration')
    if not integration:
        if method == 'OPTIONS' and 'Origin' in headers:
            
            return get_cors_response(headers)
        return make_error_response('Unable to find integration for path %s' % path, 404)
    uri = integration.get('uri') or ''
    integration_type = integration['type'].upper()
    if uri.startswith('arn:aws:apigateway:') and ':lambda:path' in uri: