I worked in two states, when I go to file it shows my total federal income amount as the amount for each state. Is that right?

$100K is correct for Ohio. 

Ohio does a convoluted tax calculation for non-residents/part year residents. It calculates tax on total income, then it calculates a non resident/part year resident credit, which it subtracts from the tax it calculated on the total income. The credit is calculated as your non-Ohio income divided by Total adjusted Income multiplied by the total tax. TurboTax (TT)   does this by allocating your income as either Ohio or non-Ohio. W-2 income will be allocated by the state name abbreviation shown in box 15 of your W-2. TT will ask you, item by item, in the state section, how much of your other income is Ohio or non-Ohio income. Make sure that your non-Ohio wages show GA (Other state postal abbreviation)  in box 15 of your W-2 screen, with the GA amount in box 16.

I can't speak specifically for how GA does it, but it is not unusual for other states to show all income and then do a percentage calculation for the actual taxable income. 

@vliv --

You didn't say which state you live in.

If you live in one state and work in another, then your resident state can tax ALL your income, regardless of where you earn it.  A non-resident state can tax income that you earn by working within its borders.  As @Hal_Al indicated, a non-resident state might use your gross overall income to determine your tax rate, but it will actually tax only your income from that state.

Your resident state will grant you a credit for taxes you pay to a non-resident state on the income taxed by both, so in the end you won't be double-taxed.

If you literally move from one state to another during the tax year, then you file a part-year resident return in each of the two states and allocate your income accordingly.