Simply integrate all the pieces apart, en add them up. This is allowed, because
int_a^c f(x)dx = int_a^b f(x)dx + int_b^c f(x)dx for all a,b,c in dom(f).
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piecewise
Graph each "piece" of the function separately, on the given domain.
yes, every continuous function is integrable.
Yes, a corner is continuous, as long as you don't have to lift your pencil up then it is a continuous function. Continuous functions just have no breaks, gaps, or holes.
They are both continuous, symmetric distribution functions.