The derivative equation is dy/dx = x² + x and y(5) = 12.

dy = (x² + x) dx

y = x³/3 + x²/2 + C

To find the value of C, substitute x = 5 and  y = 12 in the above equation.

12 = 5³/3 + 5²/2 + C

12 = 125/3 + 25/2 + C

12 = 325/6 + C

C = 12 - 325/6

C = - 253/6.

The function is y = x³/3 + x²/2  - 253/6.