12.1 no 1

Can you tell me what I'm doing wrong here?

I  think so.  When dividing the square [0,2]x[0,2] into four equal squares you get squares [0,1]x[0,1], [0,1]x[1,2], [1,2]x[0,1], [1,2]x[1,2].  It looks like you misinterpreted the questions--for example in part (A) you have supplied the value of the integral

But you should instead give the value of the Riemann sum approximation for the integral

with that partition of the square with values at the points (0,0),(1,0),(0,1),(1,1)

(25-0^2-0^2)ΔA_{11}+(25-1^2-0^2)ΔA_{21}+(25-0^2-1^2)ΔΑ_{12}+(25-1^2-1^2)ΔΑ_{22}

and since all of the ΔA's take the value 1, the correct answer for part (A) should be 

25+24+24+23=96