Shaul's genealogy is outlined in Shmuel 1:9:1, in Divrei Hayamim 1:8:29-33 and in Divrei Hayamim 1:9:35-39. There are some differences in the genealogies in the three locations, and there are different explanations, but ultimately Shaul's genealogy doesn't go all the way to Binyamin, but starts from his ancestor Afiach or possibly even a bit further back with Matar/Matri.
Why is this so?
Edit: So far I've seen that multiple Bible academics believe that this ties into the general description of Shaul in DH, much of which is negative, and this is evidence that the author of DH was a pro-Davidic, anti-Shaulic scribe. This doesn't sit well with me, because according to tradition, the author of DH is believed to have been Ezra (and perhaps also Nechemiah adding the later generations, after Ezra's death). Such a downright political bias seems uncharacteristic, to say the least.