How to evaluate the integral?

Answer:
Step-by-step explanation:
Start from the inside and work outwards, treating any other variables as constant.
[tex]\int\limits^1_{-1} {\int\limits^4_{-4} {(x^2-y^2)} dy\ dx = \int\limits^1_{-1} {(x^2y - y^3/3)^4_1} \, dx = \int\limits^1_{-1} {(3x^2-21)} \, dx[/tex]
Can you finish it from here?