The easiest is just to plug in the two cities into Google Maps. It will give you 3 routes and all are around the same distance. Just depends what you want to see.
1. I-84 to ID20 to I-15 to I-90; Hwy 212 - 886 miles
2. I-84 to Pocatello to I-15 to 26 a ID Falls. Then 26 to Alpine, WY (Google says to take 31/22 into Jackson but that's on Teton Pass and you don't want to do that). From Alpine take 89/191 into Teton Nat'l Park and continue east on 26 to Casper, WY. N on I-25/259/50 to I-90 - 864 miles
3. Pocatello to I-15 south to Hwy 30 to Kenmerer, WY to Fontenelle. Then 28 NE to 287 to 220 to Casper, WY. North on I-25/259/50 to I-90 - 900 miles
Full-timed for 16 Years . . .
Traveled 8 yr in a 2004 Newmar Dutch Star 40' Diesel
& 8 yr in a 33' Travel Supreme 5th wheel