Direction of Integration of Electrostatic force over a circular arc, direction of the resultant force changing with interchange in limits?

Problem:

A uniformly charged circular arc with linear charge density $m$ subtends angle $theta$, find the net force acting on a charge placed at its center if total charge of the arc is $Q$ and the charge at center is $q$.

Here, we take the line of symmetry for the arc and integrate the components of force acting along it i.e: $$2dfrac{kqm}rint_{0}^{theta /2}(cos x)$$ We get: $$2kqmdfrac{sin(theta / 2)}r$$

If we integrate from $theta/2$ to $0$, we get negative value ($k = 9 times 10^9$, $r$ = radius of arc)

I wanted to know, why is the sign changing when we add the same thing in different ways. Is there a rule to know how to decide the limits or its just the faulty mechanism or there is actual change in direction of force.

I was thinking that it actually rotates the axes about y axis, where positive z axis is decided by using right thumb rule hence as the force acts on x axis, the sign gets flipped. Just a speculation.