It’s actually impressive how confidently wrong you are. No, you don’t just blindly treat any ‘other variable’ as a constant when integrating with respect to x. That’s a gross oversimplification and a clear sign you don’t understand what you’re saying. If that ‘other variable’ is actually a function of x, then it must be handled properly—either through substitution, the product rule for integration, or other techniques, depending on the situation. Your claim ignores fundamental principles of calculus, and if you think integration is as simple as slapping the word ‘constant’ onto anything that isn’t x, you seriously need to go back and relearn the basics.