Count the number of a number in the picture area
Mathematica, 92 bytes

Count[Take[Characters@StringSplit@TextRecognize@Binarize[Import@#4,.9],#2,#],ToString@#3,2]&amp;


Unnamed function taking the arguments in this format: [{X1,X2}, {Y1,Y2}, N, "image.jpg"]. (Indeed, the fourth argument can be either the local file name or the URL http://i67.tinypic.com/6qh5lj.jpg.)

Import@#4 imports the image file, Binarize[...,.9] darkens all of the numbers to black, and TextRecognize (the function clearly doing the heavy lifting here!) extracts a multi-line string from the resulting image, which is split into a nested list of characters with Characters@.

Take[...,#2,#] keeps only the characters corresponding to the outlined rectangle, and Count[...,ToString@#3,2] counts the number of occurrences of N in the result.