All of Texas is CST....and I think that the CST bends around to include Indianapolis.
From someone who lives here in Indiana, Indianapolis falls in EST.
At one time, most of the state didn't follow daylight savings time so sometimes there were areas of Indiana that aligned with CST. Mainly this happened because IN is largely an agricultural state and farmers days are dictated by when the sun is up and not by a clock. The bankers and businesses in IN of course wanted to follow DST to align more with east coast businesses hours. This was changed in 2005 and now the entire state follows DST. Problems still arise here in that there are areas that follow CST, mainly the counties in the upper NW corner near Chicago and the lower SW counties.
This is still an object of contention in the state with many wanting the state to be all CST and another faction wanting to return to not observing DST. Needless to say Indiana is probably the most f***ed state when it comes to figuring out what time it is.