Final answer:
Robust australopithecines, belonging to the genus Paranthropus, went extinct by 1 million years ago (MYA), corresponding to option 'a. 1 mya'.
Step-by-step explanation:
The robust australopithecines, categorized under the genus Paranthropus, included species such as Paranthropus robustus, P. boisei, and P. aethiopicus. The gracile species of australopithecines began to appear around 4 million years ago (MYA) and disappeared by 2 MYA. The robust australopithecines continued to exist longer, with evidence suggesting that they went extinct by 1 MYA. Therefore, the correct answer to when robust australopithecines went extinct is option 'a. 1 mya'.