To solve this, we apply the power rule of integration: ∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C. For the first term, ∫ 6x² dx = 6(x³/3) = 2x³. For the second term, ∫ -4x dx = -4(x²/2) = -2x². For the third term, ∫ 3 dx = 3x. Combining these and adding the constant of integration C, we get 2x³ - 2x² + 3x + C. Option 1 is incorrect because it represents the derivative, not the integral. Option 3 has an incorrect coefficient for the first term (3 instead of 2). Option 4 has an incorrect coefficient for the second term (4 instead of 2).