(B) Let $f(x) = x|x|$.We check if the function is even or odd:$f(-x) = (-x)|-x| = -x|x| = -f(x)$.Since $f(-x) = -f(x)$,the function $f(x) = x|x|$ is a

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(B) Let $f(x) = x|x|$.We check if the function is even or odd:$f(-x) = (-x)|-x| = -x|x| = -f(x)$.Since $f(-x) = -f(x)$,the function $f(x) = x|x|$ is an odd function.According to the property of definite integrals,if $f(x)$ is an odd function,then $\int_{-a}^{a} f(x) \, dx = 0$.Therefore,$\int_{-1}^{1} x|x| \, dx = 0$.