According to the power rule of integration, ∫xⁿ dx = (xⁿ⁺¹)/(n+1) + C for n ≠ -1. Applying this to each term: ∫x³ dx = x⁴/4, ∫-4x dx = -4(x²/2) = -2x², and ∫5 dx = 5x. Summing these results and adding the constant of integration C gives x⁴/4 - 2x² + 5x + C. Option 2 is incorrect because it represents the derivative of the function. Option 3 fails to divide the coefficient 4 by the new power 2. Option 4 uses the wrong power for the first term.