完了不定詞（to have ＋過去分詞）
着眼点述語動詞より前の出来事を表す。「時のズレ」を読む。
単純形 to do：述語と同時か、それ以後。
完了形 to have done：述語より前。
He seems to be sick. = It seems that he is sick.
He seems to have been sick. = It seems that he was / has been sick.
例文
1
She is said to have been a famous singer.
彼女はかつて有名な歌手だったと言われている。
2
I'm sorry to have kept you waiting.
お待たせしてすみません。
ポイントwant / hope / intend の過去形＋to have done は「実現しなかった」を表す：I hoped to have seen her.（会いたかったが会えなかった）
確認問題
1
書き換え。 It seems that he was ill yesterday. → He seems ( ) ( ) ( ) ill yesterday.
答え
to have been（seems より前の時点なので完了不定詞）