Calories burned w/ Weight Lifting - How to count?

I have been reading that I shouldn't count my calories burned for weight lifting. I am doing Jillian Michaels Body Revolution, which is 3 circuits of various weight lifting things, with 1 minute of cardio between each set.

While I am wearing my HRM it shows that I am burning about 350 calories. So since there is some cardio in there, how would I count my calories I've burned?

I have my Jawbone synced up with MFP, so I don't want to add calories that I haven't really "earned" and eat them. I suspect that is why my weight loss has been very slow and I've been battling with the same 5 lbs for a couple of months.

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