Sung vs. sang (sing)

[richard]

English Grammar Tests, Elementary Level

ESL/EFL Test #83 "Past Participle Sentences", question 2

I would have ......... all night if I could but we all had to leave early because Carmen didn't feel good.

(a) sing
(b) sung
(c) sang
(d) singed

English Grammar Tests, Elementary Level

ESL/EFL Test #83 "Past Participle Sentences", answer 2

I would have sung all night if I could but we all had to leave early because Carmen didn't feel good.

Correct answer: (b) sung
_________________________

why sung not sing?

[Pamela]

It's future perfect in the past,that's why I would have sung but not sing (which is an infinive but not the third form of "sing").