I need to derive a general expression for an digital option position that at expiration pays (i) nothing below K₁, (ii) one (1) unit of currency between K₁ and K₂, and (ii) nothing above K₂.

The expression used these options are:

C(K) = e^rtN (d_2,K)

and

P(K) = e^rtN (-d_2,K)