Does MySql come out of the box installed in pivotal cloud foundry environment? I was told that the containers within cloud foundry are transient in nature. If so , how does it support MySQL DB installation?
Pivotal offers Cloud Foundry in a couple ways. The hosted service is called Pivotal Web Services and allows apps to bind to a MySQL service such as ClearDB -- check out the marketplace.
The on-premise offering of Pivotal Cloud Foundry provides a MySQL service as well.
MySQL itself doesn't run as an application on Cloud Foundry, it's offered as a service alongside Cloud Foundry. Cloud Foundry currently only runs stateless applications, but support for a cloud-native solution for persistent workloads is starting up, so in the future it would be possible to run MySQL as an "application" directly on Cloud Foundry.