coding style – Find the area which is between two curves

    eq1 = (x^2/400) + (y^2/256) == 1;

    eq2 = (x^2/144) - (y^2/289) == 1;

    sl = Solve({eq1, eq2}, {x, y})
    NIntegrate(eq1 - eq2, {x, s1(1), s1(2)})
    NIntegrate(eq1 - eq2, {x, s1(2), s1(3)})
    NIntegrate(eq1 - eq2, {x, s1(3), s1(4)})

Im trying to find the area which is inside the 2 curves. From s1 there are 4 solutions. What i want to do is find the area between solution 1 and 2, then 2 and 3 and then 3 and 4. When I get these values Im going too add it so it will give me the full area which is enclosed inside the two.

BUT its not working and I get zero, why do I get this value?