Step 1: Understanding Goa's Integration
- Goa was liberated from Portuguese rule in December 1961, but it did not immediately become a state of India. It was initially made a Union Territory.
- Goa was made a full-fledged state of India later, in 1987, after years of being a Union Territory.
Step 2: Analyzing the Options
- (A) 1972: Incorrect, Goa was still a Union Territory in 1972, not a state.
- (B) 1977: Incorrect, Goa remained a Union Territory during this time.
- (C) 1980: Incorrect, Goa became a state in 1987, not 1980.
- (D) 1987: Correct, Goa became a state of India in 1987.
Step 3: Conclusion
Goa became a state of the Indian Union on May 30, 1987, thus ending its status as a Union Territory.
\[
\boxed{\text{Correct Answer: (D) 1987}}
\]