To find the area between two negative z scores is, by symmetry of the bell curve, equivalent to finding the area between the corresponding positive z scores. Use the standard normal distribution table to look up the areas that go with the two corresponding positive z scores. Next subtract the smaller area from the larger area.
For example, finding the area between z1 = -2.13 and z2 = -.45, is the same as finding the area between z1* = .45 and z2* = 2.13. From the standard normal table we know that the area associated with z1* = .45 is .674. The area associated with z2* = 2.13 is .983. The desired area is the difference of these two areas from the table: .983 - .674 = .309.