Final answer:
The coordination of site surveys with plans and integration function typically falls under Geographic Information Systems (GIS), which became more prominent with the advent of computers and GIS software, superseding the use of topographic maps.
Step-by-step explanation:
The functional area which coordinates all site surveys with the plans and integration function generally falls within the realm of Geographic Information System (GIS) applications. Previously, topographic maps were the primary tools for such tasks from the 1880s until the advent of computers. With the development and spread of GIS software, the capability to integrate and analyze place-based information became far more advanced, allowing for improved coordination and planning in various sectors, including environmental management, urban planning, and engineering.