Solution

First, let's determine if the function f(x) is odd or even. A function is even if f(−x)=f(x). A function is odd if f(−x)=−f(x). Let's evaluate f(−x): f(−x)=(−x)²sin(−x) f(−x)=x²(−sinx) f(−x)=−x²sinx f(−x)=−f(x) Since f(−x)=−f(x), the functionf(x) = x²sin(x)is an odd function. For an odd function f(x), the definite integral over a symmetric interval [−a, a] is always zero: Therefore, the correct answer is option (D).