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Abstract We evaluated all two-loop conformal integrals of scalar half-BPS six-point functions in N $$ \mathcal{N} $$ = 4 SYM restricted to a configuration where all points lie on a line. Moreover, we also computed some of these integrals in the kinematical limit where adjacent points become null-separated. Our results can serve as cross-checks for future works which obtain these integrals for general kinematics or by different methods such as integrability.