1^st Moment of Area (Q): 
It measures how a shape's area is distributed in reference to an axis. Used to find out the centroid of a shape. 
Q = perpendicular dist(d) × Area(A)
The axis can be chosen as per the requirement and hence, the perpendicular distance can be either positive or negative. Hence 1^st moment of area can be either +ve or -ve depending on the location from the reference axis 
2nd Moment of Area (I): 
It is also called the moment of inertia (I) which is the capacity of a body to resist bending or angular rotation about a certain axis. 
Using the parallel axis theorem we can find the moment of inertia of any C/S using the below expression 
   
Where 
I_x and l_y = Moment of inertia about any random x-axis and y-axis respectively, I_xc and I_yc = Moment of inertia about the shape's centroidal x-axis and y-axis respectively, A = Area of shape, d₁ = Distance of reference x-axis and centroidal x-axis, d₂ = Distance of refrence y-axis and centroidal y-axis, I_y (circle) = d⁴/64 (cannot be negative). 
Hence 2^nd moment area can never be negative for circular lamina (always +ve).