Component of the integrator complex, a multiprotein complex that terminates RNA polymerase II (Pol II) transcription in the promoter-proximal region of genes (PubMed:25201415, PubMed:33243860, PubMed:38570683). The integrator complex provides a quality checkpoint during transcription elongation by driving premature transcription termination of transcripts that are unfavorably configured for transcriptional elongation: the complex terminates transcription by (1) catalyzing dephosphorylation of the C-terminal domain (CTD) of Pol II subunit POLR2A/RPB1 and SUPT5H/SPT5, (2) degrading the exiting nascent RNA transcript via endonuclease activity and (3) promoting the release of Pol II from bound DNA (PubMed:33243860). The integrator complex is also involved in terminating the synthesis of non-coding Pol II transcripts, such as enhancer RNAs (eRNAs), small nuclear RNAs (snRNAs), telomerase RNAs and long non-coding RNAs (lncRNAs) (PubMed:16239144, PubMed:26308897, PubMed:30737432). Within the integrator complex, INTS1 is involved in the post-termination step: INTS1 displaces INTS3 and the SOSS factors, allowing the integrator complex to return to the closed conformation, ready to bind to the paused elongation complex for another termination cycle (PubMed:38570683). Mediates recruitment of cytoplasmic dynein to the nuclear envelope, probably as component of the integrator complex (PubMed:23904267). {ECO:0000269|PubMed:16239144, ECO:0000269|PubMed:23904267, ECO:0000269|PubMed:25201415, ECO:0000269|PubMed:26308897, ECO:0000269|PubMed:30737432, ECO:0000269|PubMed:33243860, ECO:0000269|PubMed:38570683}. This is the function of Ensembl gene identifier ENSG00000164880 (INTS1, integrator complex subunit 1).