The viral infection that leads to the integration of its genome into the host cell's genome is called retroviral infection.

Here's why:

* Retroviruses are a type of RNA virus that use a unique process to replicate.

* They carry an enzyme called reverse transcriptase, which allows them to convert their RNA genome into DNA.

* This newly synthesized DNA can then integrate into the host cell's genome, becoming a permanent part of the host's genetic material.

Examples of retroviruses:

* HIV (Human Immunodeficiency Virus): Causes AIDS.

* HTLV-1 (Human T-lymphotropic virus type 1): Can cause leukemia and other diseases.

Important note: Not all viruses integrate their genome into the host's DNA. Some, like influenza virus, simply replicate within the host cell without integrating.