When exploring and querying inconsistent data, inconsistency measures referring to constraint violations can help the user to quantify the quality of the underlying data and query results. We showcase INCA, a system that allows the user to execute data profiling and query answering tasks in an inconsistency-aware fashion. By using data instances annotated with novel inconsistency measures based on why-provenance and polynomial provenance, it becomes possible to visualize the share of the data which is consistent or inconsistent with respect to one or multiple denial constraints. Furthermore, data exploration by constraint or by subset of constraints allows to inspect the tuple violations according to multifaceted criteria. Finally, query profiling allows to enable inconsistency-aware query results accounting for most (in-)consistent top-k and threshold query results. To the best of our knowledge, INCA is the first system to allow such an inconsistency-driven analysis of both data and query results. Such an analysis is especially fruitful for enabling selective constraint-based data cleaning and inconsistency-aware ranking of query results in data science pipelines, thus leading to more explainable outputs of those processes.