Suppose an abject moves on the path formed by $x(t)=t^3+t$ and $y(t)=t^2+1$ where distances are in feet and $t$ is in seconds

a$)$ Find the equation of the line tangent to the graph when $t=2$

b$)$ Find the speed of the object when $t=2$

c$)$ Find the distance travelled by the object from time $t=0$ to time $t=2$

d$)$ Find the area between the curve and the x $-$axis for $0t2$