Integrations are what Duo Security calls the connections to their APIs. There are two main types (so far) that are used to work with different types of data:

The Admin integration allows you to work with the users that are a part of your account. You can do things like add users, remove them, update their data and associate a Device with their account.

The primary purpose of the Auth API is to validate the codes that a user provides to complete the two-factor authorization process.

The primary purpose of the Verify API is to send the user PINs/validation codes either defined with the request or automatically generated.

The primary purpose of the Account API is to get information about the current account (including child accounts).

<?php
$int = new \DuoAuth\Integration();
$fullList = $int->findAll();

// or a single one
$integration = $int->findById('your-integration-key');
?>

And saving or creating the integration:

<?php
$int = new \DuoAuth\Integration();
$int->type = 'verify';
$int->name = 'My New Integration';
$int->save();
?>