Multiple integrals with 2 definite integral and 2 symbolic result, how can I get it?

I want to do a multiple integrals with 4 variable (a, b, x, y), but just a and b need to do definite integral with numeric, x and y still the symbolic result, how can I get it?

This is my code that I fixed it many times, so it might be illogical.

syms a b x y;
fun1= @(a,b,x,y) ...
    exp(-1i.*2.*pi.*(a.*(x-x0)+b.*(y-y0)));                    % while x0, y0 is known numbers.
f1=int(fun1,-2,2,a);
f1=int(f1,-2,2,b);

I also tried integral2 function.

f1=integral2(fun1,-2,2,-2,2);

I'm wondering that should I use int? integral2? or other function to match my propose.

This is the result I want:

f1=(...x)+(...y)

And if syms and function handle have same function will blow up "Input function must return 'double' or 'single' values. Found 'sym'." ?

Answer 1

[Dyuman Joshi]

The sytanx you used was incorrect, the correct syntax is - int(Integrand, Integration Variable, Limits of Integration)

syms a b x y x0 y0
fun1= @(a,b,x,y) exp(-1i.*2.*pi.*(a.*(x-x0)+b.*(y-y0)));    % while x0, y0 are* known numbers.
f1=int(fun1,a,-2,2);
f1=int(f1,b,-2,2)

f1 = 

%Then integrate w.r.t to x and y
f1=int(f1,x)

f1 = 

f1=int(f1,y)

f1 = 

ei in the above expressions is ei - One-argument exponential integral function)

[Jacky Wang]

It works, thank you!