Putnam 1979 B2

Problem B-2 Let $0<a<b$. Evaluate $$\lim _{t \rightarrow 0}\left\{\int_{0}^{1}[b x+a(1-x)]^{\prime} d x\right\}^{1 / t}$$ [The final answer should not involve any operations other than addition, subtraction, multiplication, division, and exponentiation.]