A single unicast index coding problem (SUICP) with symmetric neighboring interference (SNI) has equal number of K messages and K receivers, the kth receiver R_k wanting the kth message x_k and having the side-information K_k = (I_k Ux_k)^c, where I_k = {x_k-U,..., X_k-2, x_k-1} U {x_k+1, x_k+2,..., x_k+D} is the interference with D messages after and U messages before its desired message. Maleki, Cadambe and Jafar obtained the capacity of this symmetric neighboring interference single unicast index coding problem (SNI-SUICP) with (K) tending to infinity and Blasiak, Kleinberg and Lubetzky for the special case of (D = U = 1) with K being finite. In this work, for any finite K and arbitrary D we obtain the capacity for the case U = gcd(K, D + 1) - 1. Our achievability proof is constructive, i.e., we give an explicit construction of a linear index code achieving the capacity.