Commercial Fixed Wing
Flight Crew Last 90 Days 559; Flight Crew Type 10500
Confusion
ATC Issue All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Ground Incursion Taxiway
Air Traffic Control Issued New Clearance; Flight Crew Requested ATC Assistance / Clarification
Chart Or Publication; Procedure
Shortly after departure out of ZZZ; we obtained ATIS for RDU due to the short flight time. One of the ATIS NOTAMs listed Taxiway C at RDU closed between F and G.  There were numerous taxiway closures and I annotated them with the red drawing tool on my EFB 10-9 page.  Based on the ATIS; we briefed the ILS to Runway XXR.  We also briefed to expect to taxi D; A; to parking; when clearing the runway due to the C Taxiway closure NOTAM. After landing; Ground cleared us to taxi C; A; to the gate. However; taxiing clear of the runway; I went to Taxiway D based on the red area I had drawn on my EFB 10-9 page and the taxiway closure NOTAM. Half-way up Taxiway D; I noticed there were no closure markings or construction on Taxiway C.We queried Ground about our clearance and he stated 'C; A; to the gate.'  We mentioned we had taken D in error. He said 'no problem; continue D; A; to the gate.' We didn't mention the ATIS NOTAM as I wasn't sure if I had read it correctly. After aircraft shutdown; we looked at the ATIS again and noticed we had read the closure correctly and it was still listed in the current ATIS.
Air carrier Captain reported a taxiway was NOTAMed closed due to construction at RDU airport; however the NOTAM was not included in the ATIS information and ground control issued taxi instructions via the closed taxiway.