fit using parametric equations

Question

I have experimental data with two columns (x & y). I need to fit the data to two parametric equations of the form

$$y =\text{const}_1 \times \left( \frac{\int _a^{b}\sqrt{\frac{\left( 1+\gamma \sin^{2}( \phi _{m})\sin^{2}( \psi ) \right) \left( 1+\kappa \sin^{2}(\phi _{m}) \sin^{2}( \psi ) \right) }{\left( 1- \sin^{2}(\phi _{m}) \sin^{2}( \psi ) \right) \left( 1+\nu \sin^{2}(\phi _{m}) \sin^{2}( \psi ) \right) }}d\psi }{\int _{a}^{b}\sqrt{\frac{\left( 1+\gamma \sin^{2}( \phi _{m})\sin^{2}( \psi ) \right) \left( 1+\kappa \sin^{2}(\phi _{m}) \sin^{2}( \psi ) \right) }{\left( 1-\sin^{2}(\phi _{m}) \sin^{2}(\psi ) \right) }}d\psi }-\text{const}_2\right)$$

and

$$x=\text{const}_3\times \int _{a}^{b}\sqrt{\frac{1+\kappa \sin^{2}(\phi _{m}) \sin^{2}( \psi ) }{\left( 1+\gamma \sin^{2}(\phi _{m})\sin^{2}( \psi ) \right) \left( 1- \sin^{2}(\phi _{m}) \sin^{2}( \psi ) \right) }}d\psi.$$

My fit parameters are a,b,$\kappa$ & $\phi_m$. How can I fit the data using the above equations?