National integrity and unity are emphasized in the UPSC syllabus through topics on secularism, communal harmony, and integration of states. The syllabus highlights the importance of a cohesive national identity in the context of diverse cultures and languages across India. Understanding issues like regionalism, linguistic diversity, and the role of institutions in promoting unity is crucial. By instilling values of integrity, candidates are better prepared to handle public administration challenges that may threaten societal cohesion.