Do you mean I(t)= 140(t^3)/4 or I(t)= 140 t^(3/4)? I'm going to assume the latter since the former would be more simply written I(t)= 35t^3.

Also I will assume that "K"is"capital stock" although it would have been a good idea to say so!

If I(t) is the instantaneous rate of change of K(t), the derivative, then K(t) is the anti-derivative of I(t). Do you know the anti-derivative of t^n? If not, I may be completely misunderstanding your question.