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Calculus of variations with integral constraints

Hi everyone, the image is attached.

Both p(x,y) and q(x,y) are probability density functions, q(x,y) is an already known density function, my job is to minimise C[p,q] with respect to 3 conditions, they are listed in the red numbers, 1, 2, 3. Setting up the lagrange function and simplifying it up to equation (21) is fine with me, however I am lost when they mention "calculus of variations" as I have not studied, I assume (22) follows on from the calculus of variation technique they used, I was wondering where I can read about calculus of variations to help me solve problems like this with integral constraints? Thanks!