What do you mean by "constants don't effect integrals"? Unless you have some unusual meaning, they certainly do. If f(x)= g(x)+ C, then . That is, if f and g differ by the added constant, C, then their integrals differ by Cx.

Perhaps you are mis-remembering that an added constant does not change thederivative. If f(x)= g(x)+ C, then .

Or are you refering to the "constant of integration"? Because an added constant does not change thederivative, where C can be any number because for any C.