What does the protection goal Integrity (Integrität) guarantee?

That data or systems cannot be altered — maliciously or accidentally — without authorisation.

Integrity is about trusting that data hasn't changed. It covers both deliberate tampering and accidental corruption (e.g. a flipped bit in transmission).

Mechanisms, in increasing strength:

• Checksums — catch accidental errors
• Cryptographic hashes — catch any change, accidental or malicious
• MACs / digital signatures — catch changes and tie them to an identity

Note: completeness (Vollständigkeit) is treated as a part of integrity — data that's been silently truncated has lost integrity too.

Go deeper:

• Integrity (NIST glossary) — the FIPS 200 definition: guarding against improper modification or destruction.
• Data integrity (Wikipedia) — accuracy and completeness over the data lifecycle, plus the checksum/hash mechanisms the card lists.