Integrating characteristic functions.

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I need to find the radon transform of the following function. But I got stuck in finding this integral. Let $\chi$ be given by

$$\chi(t) = \begin{cases} 1 & |t|< 1/2 \\ 0 & \text{otherwise}\end{cases}$$

Then Radon transform would be obtained by this integral.

$$\int_{s_A}^{s_B}\chi(\rho -s\alpha)\chi(\rho^{'} +s \beta)\,ds$$

where $$s_A,s_B$$ are two numbers.

I have the answer for this and I am supposed to check it to see if it is right or not but each time I end up with a different answer. Could you please give me a brief hint on calculation of this integral?