See the basic property :
_{-a}∫ ^{a }f(x) dx = 0 , f(x) is odd = 2 _{0}∫^{a} f(x) dx
_{-a}∫ ^{a }f(x) dx = 0 , f(x) is odd
= 2 _{0}∫^{a} f(x) dx
So here :
The function f(x) = x^{2} sinx is odd as we know product of odd function and even function is odd function only..
Therefore the given integral value = 0.
Hence 0 is correct answer..
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This might help..