Final answer:
Option C is the best answer as it integrates quantitative analysis with the qualitative understanding of young men traveling alone to America for better opportunities during the Irish Famine.
Step-by-step explanation:
The integration of quantitative analysis into qualitative analysis concerning the history of immigrants arriving at the Port of New York during the Irish Famine would involve combining statistical data with the narrative understanding of the situation. In this context, option C, which seeks to understand how many single young men traveled to America in hope of a better life, best represents this integration. It not only addresses the qualitative reasons behind the journey but also requires quantitative data to measure the phenomenon.