다 ending in 오래 됐다 is not infinitive ending.
다 ending after a tense containing verb is 해라체(Haera-che) ending suffix.
되다 : intinitive form
된다 : present tense Haera-che
되었다/됐다 : past tense Haera-che
It is used:
To close friends or relatives of similar age, and by adults to children.
In impersonal writing (books, newspapers, and magazines) and indirect quotations ("She said that...").
In grammar books, to give examples.
In some exclamations.
Refer to https://en.wikipedia.org/wiki/Korean_speech_levels