Intelligent reflecting surface (IRS) has emerged as a promising technique to extend the wireless signal coverage of access point (AP) and improve the communication performance cost-effectively. In order to reduce the path-loss of the cascaded user-IRS-AP channels, the IRS-integrated AP architecture has been proposed to deploy the IRSs and the antenna array of the AP within the same antenna radome. To reduce the pilot overhead for estimating all IRS-involved channels, in this paper, we propose a novel codebook-based IRS reflection design for the IRS-integrated AP to enhance the coverage performance in a given area. In particular, the codebook consisting of a small number of codewords is designed offline by employing an efficient sector division strategy based on the azimuth angle. To ensure the performance of each sector, we optimize its corresponding codeword for IRS reflection pattern to maximize the sector-min-average-effective-channel-power (SMAECP) by applying the alternating optimization (AO) and semidefinite relaxation (SDR) methods. With the designed codebook, the AP performs the IRS reflection training by sequentially applying all codewords and selects the one achieving the best communication performance for data transmission. Numerical results show that our proposed codebook design can enhance the average channel power of the whole coverage area, as compared to the system without IRS. Moreover, our proposed codebook-based IRS reflection design is shown to achieve significant performance gain over other benchmark schemes in both single-user and multi-user transmissions.