1. The problem gives the derivative of a function as $f'(x) = (x^2 + 1) \sin(3x - 1)$ and asks about intervals where the function is increasing or decreasing. 2. Recall that a function $f(x)$ is increasing where $f'(x) > 0$ and decreasing where $f'(x) < 0$. 3. Since $x^2 + 1 > 0$ for all real $x$, the sign of $f'(x)$ depends solely on $\sin(3x - 1)$. 4. We analyze where $\sin(3x - 1)$ is positive or negative on the interval $-1.5 < x < 1.5$. 5. The sine function is zero at $3x - 1 = k\pi$ for integers $k$, so zeros occur at $x = \frac{1 + k\pi}{3}$. 6. Between these zeros, $\sin(3x - 1)$ alternates sign. 7. By evaluating or approximating these zeros and signs, the intervals where $f'(x) > 0$ (function increasing) correspond to intervals where $\sin(3x - 1) > 0$. 8. Comparing the given options, the intervals where $f'(x) > 0$ match option B: $(-1.341, -0.240)$ and $(0.964, 1.5)$. Final answer: The function is increasing on intervals $(-1.341, -0.240)$ and $(0.964, 1.5)$, which corresponds to option B.