Here is the current state of this ticket. Of the examples in the first attached file, the following are legitimate bugs of this type.

The first example has unnecessary questions.

sage: integrate(1/sqrt(x-q), x, 1, 2)
2 sqrt(2 - q) - 2 sqrt(1 - q) # should be this always

The third example is definitely a case for this, as of Maxima 5.19.1:

(%i19) integrate(log(q-x), x, a, b);
Is b - a positive, negative, or zero?
positive;
(%o19) (b - q) log(q - b) - (a - q) log(q - a) - b + a
(%i20) integrate(log(q-x), x, a, b);
Is b - a positive, negative, or zero?
negative;
(%o20) (b - q) log(q - b) - (a - q) log(q - a) - b + a
(%i21) integrate(log(q-x), x, a, b);
Is b - a positive, negative, or zero?
zero;
(%o21) (b - q) log(q - b) - (a - q) log(q - a) - b + a

The fifth example has MANY questions to ask, always the same answer:

(%i36) integrate(1/sqrt(q^2-x^2),x, a, b);
Is b - a positive, negative, or zero?
negative;
Is q - a positive, negative, or zero?
zero;
Is q + a positive, negative, or zero?
zero;
Is q + b positive, negative, or zero?
positive;
b a
(%o36) asin(------) - asin(------)
abs(q) abs(q)

++++++++++++++++++++++++++++++++

The following should not be considered bugs, at least not for the reason given.

The second example is okay:

sage: integrate(1/(x-q),x,1,2)

Maxima adds pi*I and/or switches q-2 to 2-q as appropriate. If we don't like those differences, that should be on a different ticket.

The fourth example is:

sage: integrate(1/(q-x^2), x)

The answers given are a constant away from each other, but look very different. This probably should be considered a bug (Maxima can't connect between logs and arctan/h stuff), but is likely to not be resolved soon, or by questions.

The last example is definitely not a bug, as for q=-1 you should get a different answer!