Which of these dynasties was the first to unite areas of modern-day China?

This was the Qing dynasty: all the previous dynasties ruled over areas visibly smaller (even by 50%) than today's area of China. The Qing, a dynasty from Manchuria was also the last dynasty.

Before this, the Qin dynasty also united a big number of areas, and in certain contexts, this could also be the correct answer (it united all of today's eastern China).