Why do you think herodotus would call his work "researches"or "inquiries"?

Herodotus would call his work "researches"or "inquiries" because he always reason events in cause-and-effect manner. He was the only scholar who study history precisely that 2500 years after, scholars are still following his footsteps. His analysis in intellectual and socio-political manner became what he is popularly known of.

Herodotus would call his work "researches" or "inquiries" because with his Histories, he was able to create a new form of study. The name of this field—history—was coined by Herodotus himself. In his native Greek, this means "inquiries" or "research".  

It's most likely choice a, it makes the most sense in my opinion.