Plotting with  the exponential (Exp) function:

ParametricPlot3D[ {t^2+3*t,Exp[t]*Cos[Exp[t]], Sqrt[t+1]}, {t,-1,1}]

An indefinite integral...

Integrate[ { 3*t^2-1, 1/t, 2/(2*t+1), 1/(t^2+1) }, t]

... and a definite one.

Integrate[ { Cos[t], Sin[t], t/Pi }, {t,0,Pi/2} ]