Question: Define a function by an integral

Hi!!

I'm trying to define a function by a definite integral. For this, first we define the following  procedure

 

 

and the map

 

So, for a given m, my desired  "function" should be fun(curva(m,t)). The problem here, is that this function not work because, for instance, for m=2 the command fun(curva(2,t)) returns the below expession, which i think is wrong (where is the expression on "sin" or "cos(2*Pi*t)" ???)

Somebody can help me??

Thanks!!!

 

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