Design a secure database system for a cybersecurity team, focusing on a Linux environment hosted on AWS. The system must ensure data integrity and protection against cyber threats. Additionally, propose a machine learning solution to detect and mitigate potential security breaches. Detail your approach, the technologies you would use, and the steps involved in the implementation.

Define Security Testing and explain its importance in the software development lifecycle. Describe the common types of security testing and provide examples of techniques and tools used in security testing.