Different from conventional phased array (PA) and multiple-input-multiple-output (MIMO) radars, frequency diverse array (FDA) experiences the additional Doppler-spread and Doppler walk phenomena caused by the coupling among frequency increment, velocity, and acceleration. In this paper, we thoroughly investigate the coherent integration issue for detecting an FDA-based maneuvering target, consisting of range migration, Doppler-spread and Doppler walk phenomena. To address these challenges, the paper presents a novel algorithm. Specifically, we first introduce a new pulse sampling interval into the FDA-based signals to propose the resampling-keystone transform (RKT) stage, which effectively correct range migration and Doppler-spread. After the inter-channel compensation and integration of the resampled signals, the Lv's distribution (LVD) stage is applied to achieve the intra-channel coherent integration of target energy. The proposed algorithm is applicable for both single-target and multi-target scenarios. Finally, several simulation results demonstrate the potential of the proposed algorithm for improved detection performance for FDA radar. Additionally, the results indicate the underlying limitations of frequency increment and acceleration, which is caused by the coupling among frequency increment, acceleration, and quadratic slow time.