Some Properties Of Definite Integrals

Parity: is odd, is even. Odd even odd. Integral of an odd function over is . Limits are symmetric, so integral .

is an odd function. On symmetric limits , the positive and negative areas cancel: integral is .

Let . Check symmetry: So is an odd function. The integral of an odd function over a symmetric interval is . Hence the value is .

We are given the sum of two integrals, . By the property of definite integrals, we know that: Thus, adding these two integrals together gives: Hence, the correct answer is option (C) .