calculating position using follower wheels

[Ether]

Question 4:

In the code block highlighted in blue at the bottom of post 11 the following code appears for calculating position and heading:

Q+=dR/2.0;
X+=dF*sin(Q)+dS*cos(Q);
Y+=dF*cos(Q)-dS*sin(Q);
Q+=dR/2.0;

Give the mathematical justification for updating the heading "Q" twice in half-steps, instead of doing it like this:

Q+=dR;
X+=dF*sin(Q)+dS*cos(Q);
Y+=dF*cos(Q)-dS*sin(Q);