In The Case Listed Above How Come Plunging In The Integrals Directly Yeilds The

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In the case listed above how come plunging in the integrals directly yeilds the same results as using the property of order of integration? Does this only work with same numbers with opposite signs (ex -2 and 2 or pi/2 and -pi/2)? Does this only work with trig? please clarify

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