How is the limit choosen in this question since it is given that the centre of cube is at origin so why is not the lower limit 0?

See the attachment.

dear it's not start at origin see carefully

here the centre is origin but cube is equally divided on both sides of origin and given total length of side of cube is a so a/2 on right of origin and a/2 on left of origin

dear listen to be carefully.....this coordinates axis is in centre of cubic axis see again

dear plz read again this que carefully and think...

try to visualize

while doing the surface integrals limits of the integration are decided by the boundary of the surface. It has nothing to do with where the centre lies.