$f:\mathbb R\rightarrow \mathbb R$ be a continuous function satisfying $f(x)=5\int_{0}^{x}f(t)dt+1$ for all $x \in \mathbb R$ I was thinking about the following problem:
Let $f:\mathbb R\rightarrow \mathbb R$ be a continuous function satisfying $f(x)=5\int_{0}^{x}f(t)dt+1$ for all $x \in \mathbb R$.Then $f(1)=?$  
Please help. Thanks in advance for your time.

Hint:  First, what is $f(0)$?  Second, consider $f'(x)$.  You get a differential equation that way.
