Reducing the burden of documentation physicians are required to do with speech understanding is a challenging and worthwhile goal with the potential to improve care. When transcripts of doctor-patient conversations are available, automatic summarization with deep neural networks is one promising solution to reducing documentation workload. We develop an ``extract-and-abstract'' approach to automatic generation of the History of Present Illness (HPI) section in clinical notes with BART: we train a classifier on annotated data to predict a clinical section each utterance is most relevant to; we then utilize the trained classifier to select only utterances from conversations relevant to HPI to be considered as input to BART for summarization; we experiment with additional filtering methods on selected utterances to further reduce input truncation due to the token limit of BART model. Results show that the generated summaries from our approach improve in both ROUGE scores and extracted medical concepts over previously published results. Considering the improvement is achieved with a relatively small set of doctor-patient conversations, we expect further improvement with more labeled data in the future.