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Let g(x)=int0^x f(t).dt,where f is such ...

Let `g(x)=int_0^x f(t).dt`,where f is such that `1/2<=f(t)<=1` for `t in [0,1]` and `0<=f(t)<=1/2` for `t in [1,2]`.Then g(2) satisfies the inequality

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`g(x)=int_0^2f(x)dt=int_0^1f(x)dt+int_1^2f(x)dt`
`Ain(0,1)`
`int_0^1 1/2dx<=int_0^1f(t)dt<=int_0^1dt`
`1/2<=int_0^1f(t)dt<=1-(1)`
`Ain(1,2)`
`int_1^2dt<=int_1^2f(t)dt<=int_1^2 1/2dx`
`0<=int_1^2f(t)dt<=1/2-(2)`
adding equation 1 and 2
...
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