How do I fit a piecewise continuous function?

The following function is defined:

if true
  % f = @(c, x_bsn) (c(1).*x_bsn.^(c(2))).*and(x_bsn>=bound2,x_bsn<=bound1)) + (c(3)-c(4).*x_bsn.^(c(5))).*(and(x_bsn>=bound3,x_bsn<bound2));
end

Where c(1)-c(5) are the coefficients that need to be determined, x_bsn is the variable and the boundaries are specified by bound1 - bound3.

Then a fit is done using:

if true
 %fit = lsqcurvefit(f,c0,x,y);
end

Where x and y are the dataset.

The problem is that the two functions don't connect,i.e., Where the one function stops, the next one doesn't continue.

How do I create a continuous fit?

Any suggestions would be much appreciated, Amoré

p.s. Doing this part of my analysis in another program is unfortunately not an option.