A) 

 is continuous, so 

 is also continuous. This means if we were to integrate 

, the same constant of integration would apply across its entire domain. Over 

, we have 

. This means that

For 

 to be continuous, we need the limit as 

 to match 

. This means we must have

Now, over 

, we have 

, so 

, which means 

.
b) Integrating over [1, 3] is easy; it's just the area of a 2x2 square. So,

c) 

 is increasing when 

, and concave upward when 

, i.e. when 

 is also increasing.
We have 

 over the intervals 

 and 

. We can additionally see that 

 only on 

 and 

.
d) Inflection points occur when 

, and at such a point, to either side the sign of the second derivative 

 changes. We see this happening at 

, for which 

, and to the left of 

 we have 

 decreasing, then increasing along the other side.
We also have 

 along the interval 

, but even if we were to allow an entire interval as a "site of inflection", we can see that 

 to either side, so concavity would not change.