Assertion A: \[ \int_{-3}^{3} (x^3 + 5)dx = 30 \] We evaluate the integral by splitting it: \[ \int_{-3}^{3} (x^3 + 5)dx = \int_{-3}^{3} x^3 dx + \int_{-3}^{3} 5 dx \] First Integral: \[ \int_{-3}^{3} x^3 dx \] Since \( x^3 \) is an odd function (i.e., \( f(-x) = -f(x) \)), its integral over a symmetric limit \([-a, a]\) is always zero: \[ \int_{-3}^{3} x^3 dx = 0 \] Second Integral: \[ \int_{-3}^{3} 5 dx = 5 \int_{-3}^{3} dx \] \[ = 5 \times (3 - (-3)) = 5 \times 6 = 30 \] Thus, \[ \int_{-3}^{3} (x^3 + 5)dx = 0 + 30 = 30 \] So, Assertion \( A \) is true. --- Reason R: \( f(x) = x^3 + 5 \) is given, and we need to check whether it is an odd function. A function is odd if: \[ f(-x) = -f(x) \] Let’s compute \( f(-x) \): \[ f(-x) = (-x)^3 + 5 = -x^3 + 5 \] Clearly, \[ f(-x) \neq -f(x) \] since \[ -f(x) = -(x^3 + 5) = -x^3 - 5 \] Thus, \( f(x) \) is not an odd function. So, Reason \( R \) is false. --- Final Answer: - \( A \) is true. - \( R \) is false. Thus, the correct option is: \[ \boxed{C} \]