Video understanding is inherently intention-driven-humans naturally focus on relevant frames based on their goals. Recent advancements in multimodal large language models (MLLMs) have enabled flexible query-driven reasoning; however, video-based frameworks like Video Chain-of-Thought lack direct training signals to effectively identify relevant frames. Current approaches often rely on heuristic methods or pseudo-label supervised annotations, which are both costly and limited in scalability across diverse scenarios. To overcome these challenges, we introduce ViaRL, the first framework to leverage rule-based reinforcement learning (RL) for optimizing frame selection in intention-driven video understanding. An iterated amplification strategy is adopted to perform alternating cyclic training in the video CoT system, where each component undergoes iterative cycles of refinement to improve its capabilities. ViaRL utilizes the answer accuracy of a downstream model as a reward signal to train a frame selector through trial-and-error, eliminating the need for expensive annotations while closely aligning with human-like learning processes. Comprehensive experiments across multiple benchmarks, including VideoMME, LVBench, and MLVU, demonstrate that ViaRL consistently delivers superior temporal grounding performance and robust generalization across diverse video understanding tasks, highlighting its effectiveness and scalability. Notably, ViaRL achieves a nearly 15\% improvement on Needle QA, a subset of MLVU, which is required to search a specific needle within a long video and regarded as one of the most suitable benchmarks for evaluating temporal grounding.