Quantum mechanics: how to sketch the wave function?

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Your function has ONE value at any ONE point x. Not two, not three, not any other number.
 
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At what point is that the value of the function?
 
at "A" from the integrated
 
all what I need to draw is the values which are on the y-axis
and that is to describe the wave function ψ

the problem now is " what is the function on (0,b)"?

I'm not sure if I can summate the two parts from (0,a) to (a,b) without any other operator such as "integral" ?

actually I think it's not correct two ,, it leads to a complicated formulas !
but that's what I could think about to get one function as what you said ,,, !

please ,
I need to more help ()