ok so i have the differential equation:

dx/dt = ((x-1)^2)*(t+1)

this is separable and separation of variables gives

integral ( dx/((x-1)^2)) = integral (t+1) dt

im told the correct answer is..

-1 / (x-1) = ((t+1)^2)/2 + c

but am wondering, why cant i go back to the differential equation and integrate the RHS as:

(t^2)/2 + t + c

why is (t+1) integrated together... why not integrate t first... and then 1... ? surely thats more simple??