Spectrum sensing is a prominent functionality to enable dynamic spectrum access (DSA) in cognitive radio (CR) networks. It provides protection to primary users (PUs) from interference and creates opportunities of spectrum access for secondary users (SUs). It should be performed efficiently to reduce the number of false alarms and missed detections. Continuous sensing for a long time incurs cost in terms of increased energy consumption; thus, spectrum sensing ought to be energy efficient to ensure the prolonged existence of CR devices. This paper focuses on using of history to help achieve energy-efficient spectrum sensing in infrastructure-based CR networks. The scheme employs an iteratively developed history processing database that is used by CRs to make decisions about spectrum sensing, subsequently resulting in reduced spectrum scanning and improved energy efficiency. Two conventional spectrum sensing schemes, i.e., energy detection (ED) and cyclostationary feature detection (CFD), are enriched by history to demonstrate the effectiveness of the proposed scheme. System-level simulations are performed to investigate the sensitivity of the proposed history-based scheme by performing detailed energy consumption analysis for the aforementioned schemes. Results demonstrate that the employment of history ensued in improved energy efficiency due to reduced spectrum scanning. This paper also suggests which spectrum sensing scheme can be the best candidate in a particular scenario by looking into computational complexity before comparative analysis is presented with other states of the art.