Final answer:
The Beaubourg Center in Paris is distinguished by the architect's attempt to integrate the design within its surroundings.
Step-by-step explanation:
The building that is distinguished by the architect's attempt to integrate the design within its surroundings is the Beaubourg Center in Paris. Designed by Richard Rogers and Renzo Piano, along with Gianfranco Franchini, the Beaubourg Center features an inside-out structure with most of the internal mechanical and functional systems exposed on the exterior. This design approach aligns with the Postmodern idea of 'deconstruction' and the philosophy of French philosopher Jacques Derrida.