In order to ensure the privacy and integrity of the data, connections between firewalls over...

Virtual Private Networks allow a trusted network to communicate with another trusted network over untrusted networks such as the Internet.

Screened Subnet: A screened subnet is essentially the same as the screened host architecture, but adds an extra strata of security by creating a network which the bastion host resides (often call perimeter network) which is separated from the internal network. A screened subnet will be deployed by adding a perimeter network in order to separate the internal network from the external. This assures that if there is a successful attack on the bastion host, the attacker is restricted to the perimeter network by the screening router that is connected between the internal and perimeter network.

Digital Certificates: Digital Certificates will be used in the intitial steps of establishing a VPN but they would not provide the encryption and integrity by themselves.

Encryption: Even thou this seems like a choice that would include the other choices, encryption by itself does not provide integrity mechanims. So encryption would satisfy only half of the requirements of the question.

Source: TIPTON, Harold F. & KRAUSE, Micki, Information Security Management Handbook, 4th edition (volume 1), 2000, CRC Press, Chapter 3, Secured Connections to External Networks (page 65).