int() is used only for symbolic integration. You use integral() or older equivalents for numeric integration. integral() should be passed a function handle.
For example, to numerically integrate sin(t) over 0 to 2, one could use
integral(@(t) sin(t), 0, 2)
In your code you have a series of problems caused by using vectors. Your "n" is a vector, so sqrt(m-n) is going to be a vector so your x is going to be a vector and your y is going to be a vector. Then you try to integrate the vector sin(y) over y from 0 to x, but x is a vector and y has already been defined through a formula.
With you trying to use y as a variable of integration when y is defined by a formula, are you implicitly wanting to solve for the "t" such that the expression for y at that value of t gives you each value from 0 to x ?
If you have a fixed numeric vector of values, you would use trapz() or a similar integral approximation routine.
