Expectation of exponential of Ito Integral

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I need to calculate the covariance of two exponentials of Ito integrals, where B is Brownian motion: $$ \text{Cov}\left[ \text{exp}\left(\int_0^t f(u)dB_u \right) , \text{exp}\left(\int_0^s f(u)dB_u \right) \right] = \mathbb{E}\left[e^{I(t)}e^{I(s)} \right] - \mathbb{E}\left[e^{I(t)} \right]\mathbb{E}\left[e^{I()} \right]$$

I am having trouble understanding how to calculate: $$\mathbb{E}\left[ \text{exp}\left(\int_0^t f(u)dB_u \right) \right] $$

Any help is very much appreciated.