What permission is required to enable integration with the API?

The correct choice is "API Enabled" because this permission specifically grants access to the Salesforce APIs, allowing an application or user to interact with Salesforce data and functionality programmatically. When this permission is assigned to a user or a connected app, they can use various APIs such as the REST API, SOAP API, Bulk API, and others to perform operations like querying, inserting, updating, or deleting records within Salesforce.

This permission is a prerequisite for any integration work that involves accessing Salesforce from external systems or applications. It ensures that only authorized users or applications can make requests to the Salesforce API, thus enforcing security and integrity in data exchange.

The other options do not specifically cover the required permission for API access: "API Access" could refer more generally to permissions that encompass using APIs, but does not directly signify the enablement of API functionalities. "Data Management" pertains more to roles dealing with data administration tasks within Salesforce, and "Integration Rights" is not a formal permission recognized in Salesforce terminology for API access.