Is someone who is currently pursuing his Integrated Master's course/ Dual Degree course (or any other 5-year degree course) considered to be a graduate student or an undergraduate student?
In terms of the literal meaning of the word, you're an undergraduate until you graduate. Then you are called a post-graduate student (British English) or graduate student (American English) if you continue studying for a higher degree, or simply a graduate if you are no longer a student.
However, your university may use these words differently or use different words altogether, and their meaning and usage also varies across countries and cultures.
This is going to depend on institution. For example two places I know which offered Honours degree (3-year Bachelor's, +1 year with research project for so-called Honours), one of them considered Honours students undergraduates, while the other considered them postgraduates. Similarly there are undergraduates who take graduate courses, and graduates who take undergraduate courses.
I imagine however if a student is enrolled in a program that results in a Masters degree, he or she would be a graduate student, no questions asked.