Contemporary IoT environments, such as smart buildings, require end-users to trust data-capturing rules published by the systems. There are several reasons why such a trust is misplaced -- IoT systems may violate the rules deliberately or IoT devices may transfer user data to a malicious third-party due to cyberattacks, leading to the loss of individuals' privacy or service integrity. To address such concerns, we propose IoT Notary, a framework to ensure trust in IoT systems and applications. IoT Notary provides secure log sealing on live sensor data to produce a verifiable `proof-of-integrity,' based on which a verifier can attest that captured sensor data adheres to the published data-capturing rules. IoT Notary is an integral part of TIPPERS, a smart space system that has been deployed at the University of California Irvine to provide various real-time location-based services on the campus. We present extensive experiments over realtime WiFi connectivity data to evaluate IoT Notary, and the results show that IoT Notary imposes nominal overheads. The secure logs only take 21% more storage, while users can verify their one day's data in less than two seconds even using a resource-limited device.