Problem IV Evaluate a double integral
$$ \iint_P 2(x^2 - y^2 + 1) dx dy $$
over a parallelogram $P$ given below. For numbers 61-70, the parallelogram is given by its vertices. For numbers 71-80, the parallelogram is given by the lines that bound it.
61. (1,0), (3,2), (2, 3), (0,1).
62. (-1,0), (0, -2), (1, 1), (0,3).
63. (0, -1), (-1, 2), (1, 4), (2, 1).
64. (1, 1), (-1, 3), (1, 4), (3, 2).
71. $x + y = 0$, $x + y = 1$, $x + 2y = 0$, $x + 2y = 1$.
72. $x - y = 0$, $x - y = -1$, $2x - y = 0$, $2x - y = 1$.
73. $x + 2y = 0$, $x + 2y = 1$, $2x + y = 0$, $2x + y = 1$.
74. $x + y = 1$, $x + y = 2$, $x - 2y = 0$, $x - 2y = 1$.