The range -37 < x <= 35 includes all integers from -36 to 35. To find the sum of all integers in this range, we can use the formula for the sum of an arithmetic series. The sum of an arithmetic series is given by (n/2) * (first term + last term), where n is the number of terms. Here, the first term is -36 and the last term is 35. The number of terms within this range is 35 - (-36) + 1 = 72. Thus, the sum is (72/2) * (-36 + 35) = 36 * (-1) = -36. Thus, this confirms the suggested option and calculations. Hence, the correct answer is 37.