Intelligent Internet of Things (IoT) provides services for machine learning applications by collecting real-time data, where data correctness crucially impacts the training accuracy of models. Data owners host incremental real-time data in the cloud and use blockchain as a public platform for data query, usage, and certification. Malicious attackers may manipulate data through methods like data poisoning, compromising model parameters. Blockchain-based data integrity verification (auditing) schemes can effectively detect and monitor such activities. However, managing the storage demands for massive on-chain data certificates poses significant challenges. Existing compressed certificate storage strategies, such as the Merkle-Hash tree (MHT), incur significant on-chain storage costs because the auxiliary paths and the entire tree structure must be uploaded during verification, resulting in an O(n) storage overhead. Polynomial commitments offer a promising alternative by reducing storage costs to hundreds of bytes. However, current polynomial commitment methods lack effective support for incremental data updates, which are essential for real-time applications. In this paper, we propose a novel polynomial commitment-based dynamic integrity verification scheme that implements cumulative commitment updates for the first time. Our scheme includes a new data block insertion and deletion strategy that maintains the original order of data blocks within polynomial commitments. Theoretical security analysis confirms the robustness of the proposed scheme, while simulation results demonstrate that it meets the efficiency requirements for blockchain-based distributed data integrity verification mechanisms.