We often add arithmetic to extend the expressiveness of query languages and study the complexity of problems such as testing query containment and finding certain answers in the framework of answering queries using views. When adding arithmetic comparisons, the complexity of such problems is higher than the complexity of their counterparts without them. It has been observed that we can achieve lower complexity if we restrict some of the comparisons in the containing query to be closed or open semi-interval comparisons. Here, focusing a) on the problem of containment for conjunctive queries with arithmetic comparisons (CQAC queries, for short), we prove upper bounds on its computational complexity and b) on the problem of computing certain answers, we find large classes of CQAC queries and views where this problem is polynomial.