Integration of haar wavelet

How I will integrate the piecewise function mentioned in the picture (replacing the variable 'x' by 's', p_i,n(s) ), with the product of (x-s)^-alpha with respect to s for each interval separately.

[Torsten]

Do you know the antiderivative of (x-a)^(n-alpha) ?

[Abdul]

This is just (x-a)^(-alpha), from the caputo definition.

[Torsten]

What about using MATLAB's "integral" for the different sections ? Of course, all parameters have to be given as numerical values.