Practice makes a man perfect. If you will practice and remember all the identities, you will slowly realise that just by looking at the form of the question you can guess which property would work. Like, whenever you have trignometric functions, you would tend you use the property for odd and even intergrals. If your limits are from -x to +x , then you will check if the function is odd or even and then solve accordingly. So, I would recommend you to practice random questions, so that you can start realising which theorem should be used in what type of question. Also, you can use more than one property, however generally the question is solvable just by using one.