To solve this expression, we need to simplify each fraction and then perform the operations in the correct order.

-13/26 = -1/2
-1/3 remains the same
-(-1)/2 = 1/2
4/21 remains the same

Now, let's add all the fractions together:

-1/2 + -1/3 + 1/2 + 4/21 + 2

To add fractions, we need to find a common denominator. In this case, the least common multiple of 2, 3, and 21 is 42.

(-1/2)(21/21) + (-1/3)(14/14) + (1/2)(21/21) + (4/21)(2/2) + 2(42/42)

-21/42 + -14/42 + 21/42 + 8/42 + 84/42

Now, we can add the numerators:

(-21 - 14 + 21 + 8 + 84)/42

72/42

Finally, we can simplify the fraction:

72/42 = 12/7

Therefore, the simplified expression is 12/7.