The photographs captured by digital cameras usually suffer from over-exposure or under-exposure problems. The Single-Exposure Correction (SEC) and Multi-Exposure Fusion (MEF) are two widely studied image processing tasks for image exposure enhancement. However, current SEC and MEF methods ignore the internal correlation between SEC and MEF, and are proposed under distinct frameworks. What's more, most MEF methods usually fail at processing a sequence containing only under-exposed or over-exposed images. To alleviate these problems, in this paper, we develop an integrated framework to simultaneously tackle the SEC and MEF tasks. Built upon the Laplacian Pyramid (LP) decomposition, we propose a novel Fusion-Correction Network (FCNet) to fuse and correct an image sequence sequentially in a multi-level scheme. In each LP level, the image sequence is feed into a Fusion block and a Correction block for consecutive image fusion and exposure correction. The corrected image is upsampled and re-composed with the high-frequency detail components in next-level, producing the base sequence for the next-level blocks. Experiments on the benchmark dataset demonstrate that our FCNet is effective on both the SEC and MEF tasks.