1.
In trigonometric function, many cases can make two square of things equal to a constant. So we can use trigonometric function as constitution when two factor are square.

2.
You can try to substitute many different value, then compare the next part and choose the easy one.

3.
Do not always try to use constitution to solve the problem, sometimes other way may be better.

From the definition, we know that if exist and have same upper bound and lower bound when the selecting point changing.Coz there will be some bad subinterval happen, but we know the number of it is countable. It does not matter after we divide the function into n which is large enough parts. The upper bound will become smaller and smaller, and the lower bound will become bigger and bigger until they become the same.Which means if the removed points is not infinity , the function still integrable.