APIGateway AWSIntegration undocumented properties

https://docs.aws.amazon.com/cdk/api/latest/docs/@aws-cdk_aws-apigateway.AwsIntegrationProps.html

The type for `service` (name) is simply `string`, while this may be adequate for services like "s3" (the given example) this does not provide adequate documentation for other services.

For DynamoDB for example, is it DynamoDB? Is it Dynamo? Dynamo_DB?
This is just one example, there is a multitude of `string` types that should undoubtedly use Enums for self-documentation.

I would open a PR to add the enums but there is no way for me to discover the proper values but trial-and-error.

It may be possible that this is for internal naming and does not correspond to the actual Service Name within AWS.. If this is the case it is a much simpler fix to convey that this is an internal service name.

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This is a 📕 documentation issue

Start with the linked AwsIntegrationProps API reference and locate the source definition for the service property in the AWS CDK repository. Check AWS's accepted service names and determine whether the reference should list valid values or explain that the name is internal; done means the property guidance removes this ambiguity.

Written by the indexing model from the issue text.