I prefer creating the test data using API calls.
In the beginning of the test, you create an empty database (in-memory or the same that is used in production), run the install script to initialize it, and then create whatever test data used by the database. Creation of the test data may be organized for example with the Object Mother pattern, so that the same data can be reused in many tests, possibly with minor variations.
You want to have the database in a known state before every test, in order to have reproducable tests without side effects. So when a test ends, you should drop the test database or roll back the transaction, so that the next test could recreate the test data always the same way, regardless of whether the previous tests passed or failed.
The reason why I would avoid importing database dumps (or similar), is that it will couple the test data with the database schema. When the database schema changes, you would also need to change or recreate the test data, which may require manual work.
If the test data is specified in code, you will have the power of your IDE's refactoring tools at your hand. When you make a change which affects the database schema, it will probably also affect the API calls, so you will anyways need to refactor the code using the API. With nearly the same effort you can also refactor the creation of the test data - especially if the refactoring can be automated (renames, introducing parameters etc.). But if the tests rely on a database dump, you would need to manually refactor the database dump in addition to refactoring the code which uses the API.
Another thing related to integration testing the database, is testing that upgrading from a previous database schema works right. For that you might want to read the book Refactoring Databases: Evolutionary Database Design or this article: http://martinfowler.com/articles/evodb.html
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