do a substitution. u = cos(x)

no. the absolute values make a difference. you need to know how the graph without the absolute values behave. any interval that will give a negative integral will now give a positive one with the absolute values there. so you have to split the interval up. you have your work cut out for this one! see the graph below

Absolute values? Yikes. Do I just integrate this as if the absolutes weren't there, and then apply them when evaluating at the endpoints?