Intelligent systems that record, analyze, and respond to events have become major parts of our lives. They are available as Decision Support (DS) for many tasks and can enhance the information on which decision-makers can base their decisions. Decision makers need to evaluate the available information, and they also have to decide whether to seek information from additional information sources. The information is often costly, and its costs and benefits must be weighted. Also, integrating information from multiple sources can complicate the decision task. Here, we study the combined decision process that chooses information sources and integrates them, if chosen, in a classification decision. In an online experiment with 75 engineering students, we manipulated the redundancy level of information received from DS with already existing information. Participants' task in two between-subjects conditions was to classify binary events with the option to access up to two DS systems. In one of the conditions, the two DSs provided non-redundant information, and in the second condition, one of them provided fully redundant information, and the other provided non-redundant information. We found that the decision to access information was not affected by whether some information was redundant (strongly correlated with already available information). Participants used the information to improve classification performance, and the improvement was significantly higher when they used non-redundant information. However, the benefits gained were smaller than predicted from a normative model. Moreover, the use of information from multiple non-correlated sources can increase mental workload, as was evident in our results, possibly because of conflicting information from different sources.